{
 "cells": [
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   "cell_type": "markdown",
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   "source": [
    "<p align=\"center\">\n",
    "    <img src=\"https://github.com/GeostatsGuy/GeostatsPy/blob/master/TCG_color_logo.png?raw=true\" width=\"220\" height=\"240\" />\n",
    "\n",
    "</p>\n",
    "\n",
    "## Data Analytics \n",
    "\n",
    "### Parametric Distributions  in Python \n",
    "\n",
    "\n",
    "#### Michael Pyrcz, Associate Professor, University of Texas at Austin \n",
    "\n",
    "##### [Twitter](https://twitter.com/geostatsguy) | [GitHub](https://github.com/GeostatsGuy) | [Website](http://michaelpyrcz.com) | [GoogleScholar](https://scholar.google.com/citations?user=QVZ20eQAAAAJ&hl=en&oi=ao) | [Book](https://www.amazon.com/Geostatistical-Reservoir-Modeling-Michael-Pyrcz/dp/0199731446) | [YouTube](https://www.youtube.com/channel/UCLqEr-xV-ceHdXXXrTId5ig)  | [LinkedIn](https://www.linkedin.com/in/michael-pyrcz-61a648a1)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Data Analytics: Parametric Distributions\n",
    "\n",
    "Here's a demonstration of making and general use of parametric distributions in Python. This demonstration is part of the resources that I include for my courses in Spatial / Subsurface Data Analytics at the Cockrell School of Engineering at the University of Texas at Austin.  \n",
    "\n",
    "#### Parametric Distributions\n",
    "\n",
    "We will cover the following distributions:\n",
    "\n",
    "* Uniform\n",
    "* Triangular\n",
    "* Gaussian\n",
    "* Log Normal\n",
    "\n",
    "We will demonstrate:\n",
    "\n",
    "* distribution parameters \n",
    "* forward and inverse operators\n",
    "* summary statistics\n",
    "\n",
    "I have a lecture on these parametric distributions available on [YouTube](https://www.youtube.com/watch?v=U7fGsqCLPHU&t=1687s).   \n",
    "\n",
    "#### Getting Started\n",
    "\n",
    "Here's the steps to get setup in Python with the GeostatsPy package:\n",
    "\n",
    "1. Install Anaconda 3 on your machine (https://www.anaconda.com/download/). \n",
    "2. From Anaconda Navigator (within Anaconda3 group), go to the environment tab, click on base (root) green arrow and open a terminal. \n",
    "3. In the terminal type: pip install geostatspy. \n",
    "4. Open Jupyter and in the top block get started by copy and pasting the code block below from this Jupyter Notebook to start using the geostatspy functionality. \n",
    "\n",
    "You will need to copy the data file to your working directory.  They are available here:\n",
    "\n",
    "* Tabular data - unconv_MV_v4.csv at https://git.io/fhHLT.\n",
    "\n",
    "#### Importing Packages\n",
    "\n",
    "We will need some standard packages. These should have been installed with Anaconda 3."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np                        # ndarrys for gridded data\n",
    "import pandas as pd                       # DataFrames for tabular data\n",
    "import os                                 # set working directory, run executables\n",
    "import matplotlib.pyplot as plt           # for plotting\n",
    "from scipy import stats                   # summary statistics\n",
    "import math                               # trigonometry etc.\n",
    "import scipy.signal as signal             # kernel for moving window calculation\n",
    "import random                             # for randon numbers\n",
    "import seaborn as sns                     # for matrix scatter plots\n",
    "from scipy import linalg                  # for linear regression\n",
    "from sklearn import preprocessing\n",
    "import geostatspy.GSLIB as GSLIB"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Set the Working Directory\n",
    "\n",
    "I always like to do this so I don't lose files and to simplify subsequent read and writes (avoid including the full address each time). "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "#os.chdir(\"c:/PGE383\")                     # set the working directory"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Uniform Distribution\n",
    "\n",
    "Let's start with the most simple distribution.\n",
    "\n",
    "* by default a random number is uniform distributed\n",
    "\n",
    "* this ensures that enough random samples (Monte Carlo simulations) will reproduce the distribution\n",
    "\n",
    "\\begin{equation}\n",
    "x_{\\alpha}^{s} = F^{-1}_x(p_{\\alpha}), \\quad X^{s} \\sim F_X\n",
    "\\end{equation}\n",
    "\n",
    "#### Random Samples\n",
    "\n",
    "Let's demonstrate the use of the command:\n",
    "\n",
    "```python\n",
    "uniform.rvs(size=n, loc = low, scale = interval, random_state = seed)\n",
    "```\n",
    "\n",
    "Where:\n",
    "\n",
    "* size is the number of samples\n",
    "\n",
    "* loc is the minimum value\n",
    "\n",
    "* scale is the range, maximum value minus the minimum value\n",
    "\n",
    "* random_state is the random number seed\n",
    "\n",
    "We will observe the convergence of the samples to a uniform distribution as the number of samples becomes large.\n",
    "\n",
    "We will make a compact set of code by looping over all the cases of number of samples\n",
    "\n",
    "* we store the number of samples cases in the list called ns\n",
    "\n",
    "* we store the samples as a list of lists, called X_uniform\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
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\n",
      "text/plain": [
       "<Figure size 432x288 with 6 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.stats import uniform\n",
    "\n",
    "low = 0.00; interval = 0.30; ns = [1e1,1e2,1e3,1e4,1e5,1e6]; X_uniform = []\n",
    "\n",
    "index = 0\n",
    "for n in ns:\n",
    "    X_uniform.append(uniform.rvs(size=int(ns[index]), loc = low, scale = interval).tolist())\n",
    "    plt.subplot(2,3,index+1)\n",
    "    GSLIB.hist_st(X_uniform[index],low,low+interval,log=False,cumul = False,bins=20,weights = None,xlabel='Values',title='Distribution, N = ' + str(int(ns[index])))\n",
    "    index = index + 1\n",
    "    \n",
    "plt.subplots_adjust(left=0.0, bottom=0.0, right=3.0, top=2.1, wspace=0.2, hspace=0.3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can observe that by drawing more Monte Carlo simulations, we more closely approximate the original uniform parametric distribution.\n",
    "\n",
    "#### Forward Distribution\n",
    "\n",
    "Let's demonstrate the forward operator. We can take any value and calculate the associated:\n",
    "\n",
    "* density (probability density function)\n",
    "* cumulative probability\n",
    "\n",
    "The transform for the probability density function is:\n",
    "\n",
    "\\begin{equation}\n",
    "p = f_x(x)\n",
    "\\end{equation}\n",
    "\n",
    "where $f_x$ is the PDF and $p$ is the density for value, $x$.\n",
    "\n",
    "and for the cumulative distribution function is:\n",
    "\n",
    "\\begin{equation}\n",
    "P = F_x(x)\n",
    "\\end{equation}\n",
    "\n",
    "where $F_x$ is the CDF and $P$ is the cumulative probability for value, $x$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x_values = np.linspace(0.0,0.3,100)\n",
    "p_values = uniform.pdf(x_values, loc = low, scale = interval)\n",
    "P_values = uniform.cdf(x_values, loc = low, scale = interval)\n",
    "\n",
    "plt.subplot(1,2,1)\n",
    "plt.plot(x_values, p_values,'r-', lw=5, alpha=0.8, label='uniform PDF'); plt.title('Uniform PDF'); plt.xlabel('Values'); plt.ylabel('Density')\n",
    "plt.xlim([0.0,0.3]); plt.grid()\n",
    "\n",
    "plt.subplot(1,2,2)\n",
    "plt.plot(x_values, P_values,'r-', lw=5, alpha=0.8, label='uniform CDF'); plt.title('Uniform CDF'); plt.xlabel('Values'); plt.ylabel('Cumulative Probability')\n",
    "plt.xlim([0.0,0.3]); plt.ylim([0,1]); plt.grid()\n",
    "\n",
    "plt.subplots_adjust(left=0.0, bottom=0.0, right=1.8, top=0.8, wspace=0.2, hspace=0.3); plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Inverse Distribution\n",
    "\n",
    "Let's know demonstrate the reverse operator for the uniform distribution:\n",
    "\n",
    "\\begin{equation}\n",
    "X = F^{-1}_X(P)\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The P90 of our uniform distribution is 0.27.\n"
     ]
    }
   ],
   "source": [
    "p = 0.90\n",
    "x = uniform.ppf(p, loc = low, scale = interval)\n",
    "print('The P' + str(round(p*100)) + ' of our uniform distribution is ' + str(x) + '.')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's repeat this over a range of percentile values, plot and compare to the forward operation result above."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "p_values = np.linspace(0.01,0.99,100)\n",
    "x_values = uniform.ppf(p_values, loc = low, scale = interval)\n",
    "plt.plot(x_values, p_values,'r-', lw=5, alpha=0.8, label='uniform pdf');  plt.title('Uniform CDF from Sampling the Inverse of Distribution, $F^{-1}_x(x)$'); plt.xlabel('Values'); plt.ylabel('Cumulative Probability')\n",
    "plt.xlim([0.0,0.3]); plt.ylim([0,1]); plt.grid()\n",
    "\n",
    "plt.subplots_adjust(left=0.0, bottom=0.0, right=1.0, top=1.1, wspace=0.2, hspace=0.3); plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "That work's the plots are the same.\n",
    "\n",
    "#### Summary Statistics\n",
    "\n",
    "We also have a couple of convience member functions to return the statistics from the parametric distribution:\n",
    "\n",
    "* mean\n",
    "* median\n",
    "* mode\n",
    "* variance\n",
    "* standard deviation\n",
    "\n",
    "Let's demonstrate a few of these methods.\n",
    "\n",
    "```python\n",
    "uniform.stats(loc = low, scale = interval, moments = 'mvsk')\n",
    "```\n",
    "\n",
    "returns a tuple with the mean, variance, skew and kurtosis (centered 1st, 2nd, 3rd and 4th moments)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Stats: mean, variance, skew and kurtosis = (array(0.15), array(0.0075), array(0.), array(-1.2))\n"
     ]
    }
   ],
   "source": [
    "print('Stats: mean, variance, skew and kurtosis = ' + str(uniform.stats(loc = low, scale = interval, moments = 'mvsk')))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can confirm this by calculating the centered variance (regular variance) with this member function:\n",
    "\n",
    "```python\n",
    "uniform.var(loc = low, scale = interval)\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The variance is 0.0075.\n"
     ]
    }
   ],
   "source": [
    "print('The variance is ' + str(round(uniform.var(loc = low, scale = interval),4)) + '.')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also directly calculate the:\n",
    "\n",
    "* standard deviation - std\n",
    "* mean - mean\n",
    "* median - median\n",
    "\n",
    "We can also calculate order of a non-centered moment. The moment method allows us to calculate an non-centered moment of any order. Try this out."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The 4th order non-centered moment is 0.00162\n"
     ]
    }
   ],
   "source": [
    "m_order = 4\n",
    "print('The ' + str(m_order) + 'th order non-centered moment is ' + str(uniform.moment(n = m_order, loc = low, scale = interval)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Symmetric Interval\n",
    "\n",
    "We can also get the symmetric interval (e.g. prediction or confidence intervals) for any alpha level. \n",
    "\n",
    "* Note the program mislabels the value as alpha, it is actually the significance level (1 - alpha)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The interval at alpha level 0.05 is [0.01 0.29]\n"
     ]
    }
   ],
   "source": [
    "level = 0.95\n",
    "print('The interval at alpha level ' + str(round(1-level,3)) + ' is ' + str(np.round(uniform.interval(alpha = level,loc = low,scale = interval),2)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Triangular Distribution\n",
    "\n",
    "The great thing about parametric distributions is that the above member functions are the same!\n",
    "\n",
    "* we can plug and play other parametric distributions and repeat the above.\n",
    "\n",
    "This time we will make it much more compact!  \n",
    "\n",
    "* we will import the triangular distribution as my_dist and call the same functions as before\n",
    "* we need a new parameter, the distribution mode (c parameter)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The mean is 0.17.\n",
      "The variance is 0.0042.\n",
      "The interval at an alpha level of 0.05 is [0.07 0.31]\n"
     ]
    },
    {
     "data": {
      "image/png": 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iItFqD3xd7vsFiTYRERERERGJgBKiIiIi0bKQNhd6oNlAM5tmZtOWLFmS5bBERERERETiQQlRERGRaC0ANiv3/abAwrADnXMTnXO9nXO9W7dWbQ0REREREZFMUEJUREQkWpOBY83bGfjZObco10GJiIiIiIjERV5VmRcRESl0ZvYQsAfQyswWABcD9QCccxOAKUB/YA6wEjghN5GKiIiIiIjEkxKiIiIiGeScO7qKfgecFlE4IiIiIiIikkRL5kVERERERERERCQ2lBAVERERERERERGR2FBCVAqbc7BmTa6jEBERERHJjJUrcx1BVpnZnWa22Mxmpug3M7vJzOaY2Qwz6xV1jCIiUvy0h6gUprlz4e674d//hrVr4aij4JRToK7+S4uIiIhIgVm5Ev7zH3jpJXjzzVxHk213A+OAe1P0HwB0Sdx2Am5N/CsiIpIxyh5JYZk1C+68E15/vWL73XfDF1/AqFFQv35OQhMRERERSVtpqU9+Pv+8v8hfWprriCLhnHvDzDpWcsghwL2JIoRvm1kLM9vEObcomghFRCQOlBCVwnHLLT4Zmsrrr8PZZ8OYMdCwYXRxiYiIiIiko6wMpk+HKVPg5Zfhl19yHVE+ag98Xe77BYm2CglRMxsIDATo0KFDZMGJiEhxUEJUCsPcuZUnQ9d7+204/XS44QbYYIOshyUiIiIiUqWFC+HZZ/1t4cJcR5PvLKTNBRqcmwhMBOjdu3egX0REpDJKiEpheOON9I/94AM49VQYNw6aNcteTCIiIiIiqZSWwquvwpNPwrRpuY6mkCwANiv3/aaAssgiIpJRqjIvhWHq1GDbxhv7YkolIf+NZ8+GgQNh6dLsxyYiIiIist6XX8LYsbD//jB8ePrJ0BYt4LDD/DZR8TYZODZRbX5n4GftHyoiIpmmGaKS/3791e+1lOzGG2HLLWHHHeGCC3y1+fLmzIEBA+DWW33yVEREREQkG9au9SuaHn00/EJ+Ko0awZ57wgEHQN++UKdO9mLME2b2ELAH0MrMFgAXA/UAnHMTgClAf2AOsBI4ITeRiohIMVNCVPLfhx8Gq262bAmdO/uv99wTrr8ezj3XJ0/Lmz/fJ0VvuQU22wwRERERkYxZuhSeeAIefxyWLEnvPiUlsPPO8Mc/Qr9+PikaI865o6vod8BpEYUjIiIxpYSo5L+wq+y9e4OV2299l13g5pthyBBYubLisYsWwUkn+aRop05ZDVVEREREYuCzz+Dhh+H554MX7lPp0AEOPhj694c2bbIbn4iIiFRKCVHJf+++G2zbaadgW69efnn84MGwfHnFvu+/90nR8eNh662zE6eIiIiIFC/n4L//hfvvD39/GqZ+fdhnH/jTn2CHHSpe0BcREZHq++qrjDyMEqKS35Yvh48/Drb36RN+/Lbbwm23wWmnwY8/Vuz7+Wc45RS46Sbo3j3zsYqIiIhI8Vm71s8Eve8+mDs3vftsvjkcfrhfFt+sWXbjExERKWbO+bzQa6/Bq6/CF19k5GGVEJX89v77UFZWsa19e2jXLvV9unaF22+HQYNg8eKKfb/84pOlY8emTqqKiIiIiKxeDU8/DffeC999V/XxJSWwxx5wxBHB7Z1EREQkfWVlvp7Myy/7RGg643A1KSEq+S1sOVLfvlXfr2NHmDTJzwhduLBi36pVcOaZcPXVsPvuGQlTRERERIrEL7/AI4/AQw8FVxyFadYMDj3UJ0Lbts1+fCIiIsXqiy/guef8bdGirD6VEqKS38IKKqU7s7NdO58UHTQIvvyyYl9pqa9Kf+WVfl8nEREREYm35ct9EvShh4L70Yfp0AH++ldfJClmleJFREQy5vvv4cUXYcoU+OSTyJ5WCVHJX0uWwLx5wfbqLHVv0wYmTvSFlj77rGLfunVw4YV+xuhBB9UuVhEREREpTMuXwwMP+EToihVVH7/DDvC3v8Fuu/ll8iIiIlI9v/4Kr7wC//ynXxmcvFViBJQQlfwVNju0a1fYcMPqPU7LljBhApxxBsycWbGvrAwuvdTvEXXEETWPVUREREQKy8qVPgl6//3pzQjdYw84/njYbrtsRyYiIlKc5s2DJ5/0idBly9K/X506sOOOsOee8Pvfw8Yb1zoUJUQlf9VmuXyyZs3glltgyBBfqCnZ1Vf7maLHHluzxxcRERGRwvDrr36P0Lvvhp9/rvzYkhLYf3+fCO3UKYroREREisvq1fCvf8ETT/hCSekqKYGdd4b99vP1X5o1y2hYSohKfnKu5gWVUmncGG66Cc4/H956K9h/001+psDJJ6sqqIiIiEixWbcOnnnGb6e0eHHlx9at67dUOuEEvy+9iIiIVM+XX8Kjj/q9QdNZibFet25wwAGw776w0UZZC08JUclPX38N331Xsa1OHb9nU200bAhjxsCIEX6/imSTJvmk6FlnKSkqIiIiUgycg9deg/Hjg4U2k9WrB4ccAscdB5tsEkV0IiIixaOsDN5+229J89//pn+/du18EvSAA6Bjx6yFV54SopKfwpbLb7edn+VZW/Xrw6hRfu/QKVOC/Q8+6Kd0DxumjfJFRERECtnMmXD99VUv0atTxydCTzwR2raNJjYREZFisXIlPPssPPwwzJ+f3n3q1/ezQA85BHr0iDz/ooSo5KdML5dPVqcOXHKJnzH6xBPB/iee8HuKXnKJP1ZERERECsfChTBuHLz4YuXHlZRA//5w0knQvn00sYmIiBSL777zk8qeegpWrEjvPltuCYcd5vfozvC+oNWhhKjkn7Ky8BmimUyIgn8DfMEFftbp/fcH+597zs8UvfJKf+VCRERERPLbypVw553wwAOwZk3lx+65JwwaBFtsEU1sIiIixWLePLjnHnj+eb9Hd1UaNvSzQQ891K/+zYMtCpUQlfzz2WewbFnFtoYN/S9NppnBmWf6pOjEicH+V1+Fc86Ba6/1MYiIiIhI/ikr80v1xo+HH36o/NheveD002H77aOJTUREpFhMn+4Tof/+d3rHb7op/OUvvlBhkyZZDa26lBCV/BO2XL5XL7/JfTaYwcCBPil6ww3B/v/+F844w/dlYg9TEREREcmcWbPg6qth9uzKj9tiC38h/He/y4uZKSIiIgXBOXjrLbjjDpgxI7379O0LRx/tx9w8rc2ihKjkn7Dl8n36ZP95/+///CzQ0aODfe+/D6eeCjffnNM9LkREREQkYelSv0/o5MmVH9eyJZxyii/aoL3hRURE0uMc/Oc/cPvtVV90BGjQAP74RzjqKOjUKfvx1VJWE6Jm1gKYBGwHOOBE59x/s/mcUuBKS+GDD4Ltmd4/NJXDD4dGjXwF+rKyin2zZsHJJ/ulWC1bRhOPiIiIiFRUVgaPPQa33AK//JL6uPr1/QXv44/XKh8REZF0OQdvvOEToZ98UvXxLVr4ZfFHHgnNm2c9vEzJ9gzRG4HnnXOHm1l9QO9EpHIzZ/pCRuU1bw5dukQXwx//6JOiF14Ia9dW7Pv8c1+F9NZboU2b6GISERERET9DZdQo+Pjjyo/bZx+/5VG7dtHEJSIiUujWzwidMAE+/bTq49u18xceDz64IGuuZC0hambNgH7A8QDOuVKgNFvPJ0UibP/QPn2i33Nir73guuvgvPP8rNXyvvoKBgzwSdH27aONS0RERCSOli/3M0Ife8x/YEulSxf//q1Xr+hiExERKXTvvedXw6azR2iXLnDccfCHPxT0VjTZnCHaCVgC3GVmPYD3gDOdcyuy+JxS6MISolEtl0/2u9/BTTfBWWfBqlUV+xYu9DNFb7kFOnbMSXgiIiIiRc85ePVVuOYa+P771Mc1ber3e//znwv6w5mIiEikZs/2idB33qn62G228XmQ3XcviuKE2Zx2VxfoBdzqnNsBWAEMSz7IzAaa2TQzm7ZkyZIshiN5b+VKv09nsigKKqXSu7dPejZtGuxbvNj/Mfjss+jjEhERESl2330H55wD559feTL04IPhiSf83mVKhoqIiFRt/nw/vh57bNXJ0G7d4IYb4N57oV+/okiGQnYToguABc659T/Zx/AJ0gqccxOdc72dc71bt26dxXAk773/PqxbV7GtbVvYdNPcxLPe9tvDbbfBhhsG+3780Rda+uij6OMSERERKUZlZfDoo3DEEb6oQypbbgl33AEjR4a/TxMREZGKli6Fq6/2BaVfeaXyY7fbzq+avece2G23okmErpe1JfPOuW/N7Gsz28o59ymwNzA7W88nRSDVcvl8+KXr2tVXWDv1VEieybx8OQwa5K+Y7LhjTsITERERKQrz58MVV/gL5ak0auQvSB91FNTNdo1YERGRIrB6NTz4INx9t1+dW5kuXXyOowiToOVl+x3E6cADiQrz84ATsvx8Usjyaf/QMB07wqRJPim6cGHFvlWr4PTTYcwY2HXXnIQnIiIiUrDKyuCBB3zRyuSCluXtvjsMHepXEYmIiEjlysrg+edh3Di/7V9lNtvM5zv22Sf6wtY5kNWEqHNuOtA7m88hRWLpUpgzJ9iey/1Dw7Rv/1tS9KuvKvaVlsLZZ8NVV/kq9SIiIiJSta++gksuqXwLoo028nud7bVXUc9WERERyZiZM/2krZkzKz+udWsYOBAOOihWKy+KP+UrhWHatGBbp07+zW++adPGL5/v0iXYt3YtDBsGU6ZEH5eIiIhIISkr88v3jj668mTon/4Ejz0Ge++tZKiIiEhVFi/2+2sff3zlydDGjf3S+CefhEMPjVUyFLK/ZF4kPfm+XD5Zy5a+0NLpp8OsWRX7ysrg4ov9Hh2HHZab+ERERETy2Tff+PdL06enPqZdO7joovxbMSQiIpKP1qzx289MmuTzEanUqQN//jMMGOBzGzGlhKjkh0JLiAI0a+b3uRoyJLjxv3N+6fzKlfB//5eT8ERERETyjnPw9NMwdmzqog5mvmDSoEG+gJKIiIhU7p134Jprglv7Jfv97+HMM6FDh2jiymNKiEruffNNsEhRSQn06pWbeKqjcWO46Sa/p9VbbwX7b7jBv9k/6SQt8RIREZF4W7rUV5B/443Ux2y2mZ852rNnZGGJiIgUrO++8xcZ//Wvyo/bcks45xytuihHCVHJvbDZodtuC02aRB9LTTRs6DcqHj4cXn012D9xoq9Cf8YZSoqKiIhIPP3733DZZfDjj6mPOeooOO00zQoVERGpyrp18NBDMGFC5cvjmzf3RaEPPdQvlZf/UUJUcm/q1GBboV21qF8fRo/2FVKfey7Yf999fqbo0KF+9quIiIhIHPz6K9x4IzzySOpjNtnEv4faccfIwhIRESlYM2f6Lfo++yz1MSUlcOSRvnp8s2bRxVZAlBCV3CorC0+I5vv+oWHq1IFLL/WzGp54Itj/+ON+pujFF+vKjIiIiBS/zz7zK2i++CL1MQcf7JfwbbBBdHGJiIgUol9+gVtugUcf9Xtyp9Kzp5+M1aVLZKEVIiVEJbfmzg0unapfH7p3z008tVVSAhdc4JfRP/hgsH/KFD+d/coroV696OMTERERyTbn/Ie166/3FW/DtGgBI0bAHntEGZmIiEhhev11vyp1yZLUx7Rs6Ys+H3CAtutLgxKiklth+4f27OmTooXKDM46y890uP32YP8rr/iZENdeCw0aRB+fiIiISLb8/LPfK/T111Mfs+uufsXMRhtFF5eIiEghWrrU5w5eein1MWZwxBF+r9CmTaOLrcApISq5FZYQ3Wmn6OPINDM4+WS/fP6mm4L9b73liyxdf72vVC8iIiJS6KZPhwsvhMWLw/vr1/czV444QjNXREREKuOcr08yZgwsW5b6uK5d/fY0224bXWxFQglRyZ21a+GDD4LthVZQqTLHHuuToldfHex77z0YNMgnTLXJsYiIiBSqsjK4916/r1lZWfgxW27ptwzq3Dna2ERERArN4sV+zHzzzdTHNGzoZ4QedZRqlNSQyl1L7sya5Suvl9e0KWy9dW7iyZYjjvCVU8Oqy8+cCaecEtxHVURERKQQ/PSTn/U5blzqZOiRR/qEqZKhIiIiqTkHzz7rx83KkqG77ur36v7rX5UMrQXNEJXcCVsu37t3eOKw0B14oL+CM3w4rFtXse+zz+Ckk/ysijZtchOfiIiISHXNmAHDhqVeIt+sGVx0Eey5Z7RxiYiIFJolS/ys0P/8J/UxzZv7eiQqmpQRRZh5koIxdWqwrZiWyyfbZx+47rrwglFffgkDBsDChZGHJSIiIlItzsGDD/oLuqmSoT16+GOUDBUREanciy/CX/5SeTJ0v/3gscegf38lQzNECVHJjVWr/KyCZMVQUKkyu+0GN97o9xVNtnChT4p+9VX0cYlIRpnZ/mb2qZnNMbNhIf3NzewZM/vQzGaZ2Qm5iFNEpNpWroQLLoCxY4OrXtY77ji47TZo2zba2ERERArJsmW+GOGFF6YunLTRRn7MvfJK2HDDaOMrckqISm588IEvqlRemzbQoUNu4olSnz4wfjw0aRLsW7zYz7b4/PPo4xKRjDCzOsB44ACgG3C0mXVLOuw0YLZzrgewB3CdmYVMHxcRySPz5sHf/gYvvxze36yZv/B7+ulQVztziYiIpPTf//pZoS++mPqYAw7we4X26xddXDGihKjkRqrl8nGZ+t29O0yY4PcASbZ0KZx8si86JSKFqC8wxzk3zzlXCjwMHJJ0jAOampkBTYClQNJVIhGRPPLKK3D88alXsmy/PTz0EPzud5GGJSIiUlBKS2HMGH/xcMmS8GNatvTb7V1+ub/YKFmhhKjkRlhBpb59o48jl7beGm6/HVq1CvYtWwanngrvvx99XCJSW+2Br8t9vyDRVt44YBtgIfARcKZzLkV5ZhGRHCorg5tvhvPP98vlwxx1FEycCBtvHG1sIiIihWTOHL/S4uGHUx+z997wyCPw+99HF1dMKSEq0fv5Z19ZPVkxF1RKpVMnmDQJNtkk2Ldypb9q9N//Rh+XiNRG2FR3l/T9fsB0oB3QExhnZoHLv2Y20Mymmdm0JamuIIuIZMvPP/v3IvfcE97fqBFcdRWcey7UqxdtbCIiIoXCOb+K4thjYe7c8GOaNPEzQkePhhYtIg0vrpQQlehNm+b/IJS3+eZ+D9E42nRTnxQN2z/111/hrLPg1Vejj0tEamoBsFm57zfFzwQt7wTgCefNAb4Atk5+IOfcROdcb+dc79atW2ctYBGRgPWzWN55J7y/Y0e4917Yd99IwxIRESkoP/4IQ4b4JfClpeHH9O0L//iH3zM0LtsI5gElRCV6YW+si726fFU23tgvn+/cOdi3di0MHQrPPRd9XCJSE1OBLma2RaJQ0lHA5KRj5gN7A5jZxsBWwLxIoxQRSeWVV+CEE2Bh8rWchD339LNGt9gi2rhEREQKydSpcPTR8Oab4f316sHZZ8O4cdp2JgdU/lGil6qgUtxttJHff+v002H27Ip9ZWUwciSsXg2HHpqb+EQkLc65tWY2GHgBqAPc6ZybZWanJPonAJcDd5vZR/gl9kOdc9/nLGgREfDvN26/3d/CmMGgQb64kmawiIiIhFu3Dm67De66K7g6dr1OneDKK6FLl2hjk/9RQlSi9e238PXXFdtKSmDHHXMTT75p3hxuucVPqZ8+vWKfc/4P5qpVcMwxuYhORNLknJsCTElqm1Du64WA1pmKSP5YtQouvtjPDg3TtKnfL3SXXaKNS4qOme0P3Ii/aDjJOTc6qb85cD/QAf95dYxz7q7IAxURqYnFi2H4cPjgg9TH/OUvcMYZ0KBBdHFJgJbMS7TCqstvvTU0C9QSia8mTXw111TbCIwdC3fckfpKk4iIiEh1fPcd/P3vqZOhnTr5/UKVDJVaMrM6wHjgAKAbcLSZdUs67DRgtnOuB7AHcF1iCxoRkfz21lt+8lKqZGjz5nD99XDeeUqG5gElRCVaWi6fnkaN/B/Kfv3C+2+91SdNlRQVERGR2vjoI1886bPPwvv32APuvhs22yy8X6R6+gJznHPznHOlwMPAIUnHOKCpmRnQBFgKrI02TBGRali3DsaP97M+f/op/Jgdd/SV5nffPdLQJDUlRCU6zoXPEO3bN/pYCkH9+nDNNamrt957L1x7rd/vS0RERKS6XnwRTj4Zli4N7z/pJP9epHHjaOOSYtYeKL9/1oJEW3njgG2AhcBHwJnOOb3hFZH89MMPfn/tu1Ls7FFSAqec4ic1tWkTbWxSKe0hKtH54gv/x6K8evWgR4/cxFMI6taFK67wM0affjrY/8gjfs+vESOgTp3o4xMREZHC4xxMmuQLPoSpXx8uvRT+8Ido45I4CKvGlbzkaT9gOrAX0Bl4ycz+7ZxbVuGBzAYCAwE6dOiQ+UhFRKrywQdwwQXwfYraqK1a+f23e/WKNi5Ji2aISnTCZof26AENG0YfSyEpKfGbMh91VHj/M8/4/jVroo1LRERECk9pKYwcmToZ2rq1T5YqGSrZsQAov//CpviZoOWdADzhvDnAF8DWyQ/knJvonOvtnOvdunXrrAUsIhLgHNx/v19lkSoZuvPO8OCDSobmMc0QlehouXzNlZTAOef4JWt33hnsf/llWL3aL2urrz3nRUREJMTPP/v3E9Onh/d36wbXXeeToiLZMRXoYmZbAN8ARwHHJB0zH9gb+LeZbQxsBcyLNEoRkVRWroTLLvOfwcOUlPhE6Qkn+K8lb+nVkWisWwfvvRdsV0Gl9Jn5vUkGDw7v/89/4Mwz/R9oERERkfIWLPAfzlIlQ/feGyZOVDJUsso5txYYDLwAfAw84pybZWanmNkpicMuB3Y1s4+AfwFDnXMppmCJiERo/nw4/vjUydANN4Rx4+Dvf1cytABohqhE4+OPYcWKim0bbOBnIkj1HH+8nyl6zTXBvqlTfcL0xhuhadPIQxMREZE89NFHcNZZqSvfnnACnHqqPrxJJJxzU4ApSW0Tyn29EEhRVVREJEfeeAMuuiiY11ivRw8YNUqFkwqI3vVINMKWy++4owoB1dSRR/r9v8I+uMyY4avYpfrQIyIiIvHx6qt+6V7Y+4I6dfz7idNOUzJUREQkTFmZ31v77LNTJ0OPOcbvza1kaEHROx+JRlhCVMvla+fgg30F+rCk8qefwsCBsGRJ9HGJiIhIfnjkETj/fF9IKVmTJn5Z38EHRx+XiIhIIVi5EoYOhQkTwvsbNvRV5M8+G+pqAXahUUJUsu/XX/2sxWQqqFR7++4L114L9eoF++bNg5NOgkWLoo9LREREcqesDG6+2W+v41ywv21bX6RRF6dFRETCLVjgt6t79dXw/s02g3vu8Z/JpSApISrZ9+GHwZkJLVtCp065iafY9Ovn9wxt2DDYt2ABDBjgN38WERGR4rdmDVxyif+QFmabbXyf3oeJiIiEmzoVjj3WTzIKs9tucO+90LlztHFJRmU1IWpmX5rZR2Y23cymZfO5JI+FLZfv29dXTZfM6NvXL3vbYINg33ff+aTonDnRxyUiIiLRWbnSF0+aMiW8/3e/83ucbbRRtHGJiIgUikcf9XtrL1sW3n/iiTB2rIoYF4EoZoju6Zzr6ZzrHcFzST5KlRCVzOrZE269FZo1C/YtXer3FJ09O/KwREREJAI//uiLKr79dnj/n/7kP8A1bhxpWCIiIgVh7VoYPRquvtpvPZOsUSPfN2iQChEWCb2Kkl3LlsEnnwTbtWdVdnTrBrff7rckSLZsmf+gNH165GGJiIhIFi1aBH//e+oLnwMHwvDh4YUYRURE4m7ZMjjjDHjssfD+du3grrtg772jjUuyKtsJUQe8aGbvmdnAsAPMbKCZTTOzaUtUEbv4vPde8OrKppvCJpvkJp446NwZJk2CjTcO9q1c6af/v/NO9HGJiIhI5s2b55fvhe0XXlICI0b4hKi2KhIREQmaPx9OOCF8ZStAr15+v9Att4w2Lsm6bCdEf+ec6wUcAJxmZv2SD3DOTXTO9XbO9W7dunWWw5HITZ0abNNy+ezr0MEnRTfdNNj3668wZAi8/nrkYYmIiEgGzZzp9wkPm1RQvz6MGeOXyouIiEjQ++/7SvJffRXef9hhMH48tGgRZVQSkawmRJ1zCxP/LgaeBJQJi5uwqyxaLh+NTTbxSdGwKrJr1sB558ELL0Qfl4iIiNTeu+/CqaeGF31o0sR/gOsXmIsgIiIi4AsQDhoUPo6WlMD558OFF0K9etHHJpHIWkLUzDYws6brvwb2BWZm6/kkDy1ZAl9+GWzvrfpakWnVCiZOhK23DvaVlflldE8/HX1cIiIiUnOvvAJnngmrVgX7WrXyF0R32CH6uERERPKdc3DbbTBypC+klGyDDeDGG+HII6OPTSKVzRmiGwP/MbMPgXeBfzrnns/i80m+CVsu37UrbLhh9LHEWYsWMGEC9OgR7HMOLr8cHn448rBERESkBp59FoYN86s9km22Gdx5p/Y5ExERCVNa6hOht98e3t++vS+etMsu0cYlOVE3Ww/snJsHhGRgJDbClstr/9DcaNIExo2Dc84Jf13GjPEFl048MfrYREREJD2PPALXXBPe17WrH+tbtow2JhERkUKwfDmce64v/Byme3e47jpN4IqRbBdVkrhyTgnRfNOoEdxwQ+r9xG65xe835lykYYmIiEga7r47dTK0Rw+//E/JUBERkaBFi+Dvf0+dDN13X7+qUsnQWFFCVLJj/nxYvLhiW5060LNnTsKRhPr1/YepffcN77/rLn9VrKws2rhEREQknHP+ouW4ceH9u+7qL2g2bRptXCIiIoXgs8/ghBNg3rzw/hNPhCuu8J+VJVaytmReYi5sduj220PjxtHHIhXVrev/4DdsCJMnB/sfftgvnx8xwlfXExERkdxwDq6/Hh58MLx/r73gyitVAVdERCTMu+/6ZfIrVwb76tSB4cPh4IOjj0vygrIdkh1hBZW0XD5/lJT4hGeqynmTJ/v+sKp7IiIikn1lZXD11amToQcdBKNGKRkqIiIS5rnn4IwzwpOhjRv7SvJKhsaaZohK5pWVwbRpwXYlRPNLSQmcd54fDO6+O9j/4ouwejWMHq3lAyIiIlEqK/OrOcJWcoC/oHnuuVrJISIiEub++339jDCtW/tkaNeukYYk+UfvoiTzPv0Uli2r2NaoEWy7bW7ikdTMYPBgGDQovP+NN2DIEFi1KtKwREREYmvdOrj44tTJ0OOO8xc0lQwVERGpqKzMJztTJUM7dfJ1M5QMFZQQlWwI2z90hx20pCufnXginH12eN+77/qk6S+/RBuTiIhI3KxbBxdd5Jf5hRk40I/JZtHGJSIiku/WroVLLoH77gvv32EHmDQJ2raNNCzJX0qISuaFJUS1XD7/HXOM31Q67EPWhx/CqafCzz9HH5eIiEgcrF3rx+EXXwzvHzzYJ0SVDBUREalo9Wo45xyYMiW8f6+9YPx4aNYs2rgkrykhKplVWgrTpwfblRAtDIceCpdfHr4M7+OP/QexH36IPi4REZFitmYNXHghvPxyeP/ZZ8Pxx0cakoiISEFYvhxOOw3efDO8/4gjVBdDQikhKpn10Ufw668V21q0gC23zEk4UgP77w/XXBO+xcHcuTBgAHz7bfRxiYiIFKO1a30y9JVXwvvPP9+v4hAREZGKfvjBT9r58MPw/lNO8eOo9t2WEPpfIZkVtly+Tx/9ASo0e+wB118PDRoE+77+2idF58+PPCwREZGisj4Z+uqr4f0XXOAryouIiEhFCxfC3/8On38e7Csp8ePrgAHaakZSUpZKMmvq1GBbnz7RxyG1t/POMG4cNG4c7Pv2WzjpJJg3L/q4REREikFVM0OHD4c//znamERERArBF1/4ZOeCBcG+evVg1Cg47LDo45KCooSoZM6KFTBzZrB9p52ij0UyY4cdYMKE8M2nf/jBJ0U//jj6uERERArZunUwYkR4MtQMRo70+3qLiIhIRZ984j+HLl4c7GvUCG68EfbeO/q4pOAoISqZ8957UFZWsa1dO2jfPjfxSGZ06wa33QYtWwb7fv7Z78syY0b0cYlkmZkNNrMNcx2HiBSZsjK46KLUBZQuuggOPjjamESqSWOkiOTEhx/CySfDTz8F+5o185N5VNBZ0qSEqGSOlssXry5d4PbboU2bYN+KFTBoUPj+sSKFrS0w1cweMbP9zbQBkYjUUlkZXHopvPhieP+IEUqGSqHQGCki0Xr3XV9NfsWKYF+rVjBpEmy7bfRxScFSQlQyJywhpqszxWPzzf0gEzbjd/VqGDIE/v3vyMMSyRbn3AigC3AHcDzwuZldZWadcxqYiBSmsjK46ir45z/D+y+8EP70p0hDEqkpjZEiEql//9t/3ly9OtjXrh3ccQd06hR5WFLYlBCVzFi6FObODbZrhmhxadfOJ0W32CLYV1oK554LL70UfVwiWeKcc8C3idtaYEPgMTO7JqeBiUhhcQ6uvRaeeiq8/4ILVPxBCo7GSBGJxL/+5T9nlpYG+zp18slQbdMnNaCEqGRG2HL5zp3D952Uwta6NUycCF27BvvWrfNVcSdPjj4ukQwzszPM7D3gGuBNYHvn3KnAjoBKP4tIepzzBR4efTS8/7zzVE1eCo7GSBGJxHPP+YuG69YF+7bayn8ubd06+rikKNTNdQBSJLRcPl423NAXWjrjDPjoo4p9ZWVw2WV+OcORR+YmPpHMaAUc5pz7qnyjc67MzA7MUUwiUmhuvx3uvz+878wz4S9/iTYekczQGCki2TV5Mlx+ub+wmKx7d3+xsWnT6OOSoqEZolJ7zikhGkdNm8L48dC7d3j/NdfAPfdEG5NIZm2R/EHPzO4DcM59nJuQRKSg3Huvn70SZtAg+Nvfoo1HJHM0RopI9jzxhJ9kE5YM7d0bxo1TMlRqTQlRqb1vvoFFiyq2lZRAr165iUei07ixvzK3227h/TffDLfeGj6QieS/CmUqzawOfimgiEjVHn0UbropvG/AADjxxGjjEcksjZEikh2PPuqLEIbZZRf/+bNx42hjkqKkhKjUXtjs0O22gw02iD4WiV6DBr5QxD77hPffcQdcf72SolIwzOwCM1sOdDezZYnbcmAx8HSOwxORQvDPf8LVV4f3/d//wcknRxuPSIZojBSRrPrHP1KPn/36wXXX+c+fIhmghKjUXlhBJVWXj5d69eDKK+HAFFtGPfigv8pXVhZtXCI14Jwb5ZxrClzrnGuWuDV1zm3knLsg1/GJSJ579VW49NLwvj//2e8bahZtTCIZojFSRLLmoYf8RJswe+3lE6X160cbkxQ1FVWS2ikrC0+Iav/Q+KlTB0aOhEaNwivpPvkkrFoFl1wCdfWnR/KXmW3tnPsEeNTMAnt/OOfez0FYIlII3n0XLrww/AJg//4wdKiSoVLQNEaKSFY89JCf/Rlmn33giiv0GVIyTv+jpHbmzIGffqrY1qABbL99TsKRHCspgfPP90nRe+8N9j//vK8+f9VVuron+ewc4CQg7F2ZA/aKNhwRKQgzZsA558CaNcG+vfaCiy/246RIYdMYKSKZVVkydP/9/aqLOnWijUliQQlRqZ2w2aE9eyrZFWdmcPrpPil6223B/tdeg7PPhjFjoGHDyMMTqYpz7qTEv3vmOhYRKRBz5vil8KtWBft22cXPbNGHOSkCGiNFJKP+8Y/UydD+/f3qQl1MlCxRQlRqJ6ygkpbLixmcdJKv/nf99cH+t9/2SdMbblDxLck7ZnZYZf3OuSeiikVECsA338DgwbB8ebCvRw+45hpdKJaioTFSRDLmkUdS7xmqZKhEQAlRqbk1a+D9kG2ClBCV9f76Vz9TdNSoYJX5Dz6AU0+FceOgWbPcxCcS7qBK+hygD3si4v3wA5x2Gnz/fbCva1d/4a9Ro8jDEskijZEiUntPPOEvGIZRMlQiooSo1NysWcGlYc2awVZb5SYeyU+HHeaXxl9ySbDIxOzZMHAgjB8PG22Uk/BEkjnnTsh1DCJSAH75xa92WLAg2Nehg7/g17Rp9HGJZJHGSBGptcmTfU2JMEqGSoSUEJWaC1su37u3/nhJUP/+Pil64YWwdm3Fvjlz/PL6W2+FjTfOTXwi5ZjZ/znn7jezs8P6nXNjo45JRPLMr7/6/bA/+yzY16YN3HILtGwZfVwiWaYxUkRqZcoUuPzy8L799lMyVCKl/2lSc2EFlfr0iT4OKQx77QVjx4bvozZ/PgwYED7LRiR66ze2bZriViUz29/MPjWzOWY2LMUxe5jZdDObZWavZyJwEYlAWRmMGBG+bVCzZn5maNu20cclEo1aj5EiElMvv+wTnslbqQHsuy9cdpmSoRIpzRCVmlm1Cj76KNiu/UOlMrvu6j8oDhkCK1dW7Fu0yCdFb7kFOnXKSXgiAM652xL/XlqT+5tZHWA88AdgATDVzCY752aXO6YFcAuwv3Nuvpm1qXXgIpJ9zsHo0fDqq8G+Ro3gpps0hklRq+0YKSIx9cYbMHx4cAs18BNnLrsM6tSJPi6JNaXfpWY++CC49LlNG79nlkhlevXySc+wfdW+/97vKfrpp9HHJZLEzDqZ2TNmtsTMFpvZ02aWTqajLzDHOTfPOVcKPAwcknTMMcATzrn5AM65xZmNXkSy4vbbfSGIZHXr+kq5220XfUwiOVCLMVJE4ubtt2HoUFi3LtjXrx9ceaUfR0UipoSo1EzY/qF9+4JZ9LFI4dluO7jtNthww2DfTz/BySfDjBmRhyWS5EHgEWAToB3wKPBQGvdrD3xd7vsFibbyugIbmtlrZvaemR0b9kBmNtDMppnZtCVLllT7BEQkgx5/HCZODO+77DLYeedo4xHJrZqOkSISJ++/D+ecA2vWBPt23dWvuqhXL/q4RIggIWpmdczsAzN7NtvPJRFKlRAVSVfXrn6mTZuQlcK//AKnnQbTpkUfl8hvzDl3n3NubeJ2PxCy6VHwfiFtyferC+wI/BHYD7jIzLoG7uTcROdcb+dc79atW1c3fhHJlNdfh6uvDu87+2y/95lIvNR0jBSRuJg922+V9uuvwb7evf3KirD6EiIRiWKG6JnAxxE8j0Tlp5/Cq6qqoJJUV8eOMGkStGsX7Fu1Cs44A958M/KwJN7MrKWZtQReNbNhZtbRzDY3s/OBf6bxEAuAzcp9vymwMOSY551zK5xz3wNvAD0yEb+IZNiMGXDBBeH7nh13HBxzTPQxieRIBsZIEYmDuXNh8OBg3QiA7t19sd0GDaKPS6ScrCZEzWxT/OyXSdl8HolY2Ky9jh1Bs5ekJtq180nRjh2DfaWlfonFv/4VeVgSa+8B04C/ACcDrwKvAacCJ6Rx/6lAFzPbwszqA0cBk5OOeRrY3czqmlljYCd08VAk/8yfD2ed5cejZAce6D/sicRLbcdIzGx/M/vUzOaY2bAUx+xhZtPNbJaZvZ6Z0EUkEl9/DYMGwbJlwb5ttvEFCBs3jj4ukSTZ3rn2BuB8IKR6ihQsLZeXTGvTxu/LNnhwcPbx2rV+Zs7FF8Mf/5ib+CRWnHNb1PL+a81sMPACUAe40zk3y8xOSfRPcM59bGbPAzOAMmCSc25mbWMXkQz64Qc/Lv38c7Bv111hxAjtnS6xU9sx0szqAOOBP+BXS0w1s8nOudnljmkB3ALs75ybb2Yh+yuJSF5avNgnQ3/4IdjXqROMGwdNmkQfl0iIrCVEzexAYLFz7j0z26OS4wYCAwE6qEJ5YQhLiGq5vNRWy5YwYYJfJj8zKS9UVuYToqtWweGH5yY+iSUz2w7oBjRc3+acu7eq+znnpgBTktomJH1/LXBtZiIVkYxaudLve7YwebcL/OyW0aNVEVdir4ZjZF9gjnNuXuIxHgYOAWaXO+YY4Ann3PzEYy7OZNwikiU//uiToYsWBfs22wxuuQWaN48+LpEUsrlk/nfAwWb2JfAwsJeZ3Z98kApGFJhFi2DBgoptJSWw4465iUeKS7NmfqDs1Su8f/RouLfKXJRIRpjZxcDNiduewDXAwTkNSkSyb906GD4cPg7ZxaJdO7jxRi31k9irxRjZHvi63PcLEm3ldQU2NLPXzOw9Mzs2AyGLSDatWOEntnz5ZbCvTRv/Ga9Vq8jDEqlM1hKizrkLnHObOuc64vdPe8U593/Zej6JyNSpwbatt/aJLJFMaNzY7yuz667h/TfdBLfdBk6FTCXrDgf2Br51zp2AL3qk3d9Fiplzvurtv/8d7Gve3C/1a9ky+rhE8k9Nx8iwfSaS39TVBXbE16LYD7jIzLoGHshsoJlNM7NpS5YsqVbwIpJB6+s+hF1I3HBDuPVW2GST6OMSqUIUVealmGj/UIlCw4YwZgzstVd4/+23ww03KCkq2bbKOVcGrDWzZsBioFOOYxKRbLrvPnjssWB7/fp+3NH2TiLr1XSMXABsVu77TYHkvSkWAM8751Y4574H3sAnXCvQSkORPLBuHVx4YXjh5Q028BcSN988+rhE0hBJQtQ595pz7sAonkuyyLnwGaJKiEo21K8Po0ZB//7h/Q884PvLyqKNS+JkWqKww+34qrrvAyFXhUSkKLz8sl+FkMwMrrwStt8++phE8ldNx8ipQBcz28LM6uNXEk5OOuZpYHczq2tmjYGdgJCpZyKSU8758fG114J9DRr4LWa22irysETSpd3gJX1ffBGsFle/PvQIXLAVyYw6deCSS6BRI3j88WD/E0/A6tW+4FKdOpGHJ8XNOTco8eWEREX4Zs65GbmMSUSyZMYMGDkyvO/ss2HPPaONRyTP1XSMdM6tNbPBwAtAHeBO59wsMzsl0T/BOfdx4jFnAGXAJOfczNSPKiI5MW4cTE6+noH/XHbttdCzZ+QhiVSHEqKSvnfeCbZ17+6v/ohkS0kJDBvmk6L3B+qywZQpPil6xRU+QS+SQWZ2GLAbfn+z/+A/nIlIMfnmG5/0LC0N9h19tL+JSEBNx0jn3BRgSlLbhKTvrwWuzUykIpJxDzwA99wTbDeDyy5LXQ9CJI9oD1FJn5bLS66YwZlnwsCB4f2vvALnnusToyIZYma3AKcAHwEzgZPNbHxuoxKRjFq2zI8vP/0U7NtjDzjrrKgjEikIGiNFYmzKFLj++vC+886D/faLNh6RGtIMUUnPunXw3nvBdiVEJSpmPiHasGH4Hm9vvQVnnOGLXjRuHHl4UpR+D2znnK/eZWb34D/4iUgxWLMGzj8fvvwy2Netm195UKK5AyIpaIwUiaO33oJLLw3vGzgQjjwy2nhEakHv8iQ9s2fDihUV2zbYALbZJjfxSHwde6xfQh/m/ffh1FP9jB+R2vsUKF9SejO0ZF6kODjnC/OFVcVt29bPfGnYMPq4RAqHxkiRuJk1C4YO9ZOlkh1+OJx0UvQxidSCEqKSnrDl8jvuqEI2khuHH+6LLYXN3Jk1C04+GZYujTwsKQ5m9oyZTQY2Aj42s9fM7DV8hdvWOQ1ORDLjvvvCC0FssIGvirvRRtHHJFIANEaKxNT8+X6LmVWrgn177+1XXJhFH5dILWjJvKQnrKDSTjtFH4fIegce6GfvDB8evEr5+ef+CuWtt0KbNrmJTwrZmFwHICJZ9NprcPPNwfaSErj6aujcOfKQRAqIxkiRuFm6FAYPDt9ve8cd4fLLtcWMFCQlRKVqq1fDjJAVMH36RB+LSHn77OOTouefH6wO/NVXMGCAT4q2b5+b+KQgOedeX/+1mW0MrP9j965zbnFuohKRjPj0Uxgxwi+ZTzZsGOy8c/QxiRQQjZEiMbNypZ8ZunBhsK9rV7juOqhfP/q4RDJAaXyp2ocf+sID5bVqBVtskZt4RMrbbTdfZKlRo2DfwoU+KRpWMEOkCmZ2JPAucARwJPCOmR2e26hEpMa+/95XjV+9Oth3zDFw2GHRxyRSoDRGisTA2rX+YuHHHwf72rXzn8GaNIk+LpEMSSshamaPm9kfzUwJ1Dh6991gW58+2iNE8kfv3jB+fPiAvGSJXz7/2WfRxyWFbjjQxzl3nHPuWKAvcFGOYxKRmvj1Vzj7bFgcMoFtt91gyJDIQxIpcBojRYrZ+uKDb70V7GvWzG8906pV9HGJZFC6Cc5bgWOAz81stJltncWYJN+EFVTScnnJN927w8SJsOGGwb4ff/SFlmbOjD4uKWQlScv/fkArK0QKj3Nw2WUwe3awb8st4aqrtPeZSPVpjBQpZpMmwdNPB9sbNIAbboDNN488JJFMS2vQcs697Jz7K9AL+BJ4yczeMrMTzKxeNgOUHFu2LHyKfN++0cciUpWuXX1SNOxq5fLlMGgQvP9+9HFJoXrezF4ws+PN7Hjgn8CUHMckItV1113wwgvB9pYt4frroXHj6GMSKXwaI0WK1bPPwm23BdtLSvxFxO7do49JJAvSvopnZhsBxwMDgA+AG/EJ0peyEpnkh2nTgoUHOnSAtm1zE49IVbbYwl/R3GSTYN/Klb5CYtjSD5FyzMyAm4DbgO5AD2Cic25oTgMTkep59VW45ZZge716MGZM+FghIpXSGClSxN5911eND3P++fD730cbj0gWpVVl3syeALYG7gMOcs4tSnT9w8ymZSs4yQNaLi+FaNNNfVL01FNh/vyKfaWlfh+5UaNgzz1zE5/kPeecM7OnnHM7Ak/kOh4RqYHPPoOLUmxpeNFFmuEiUkMaI0WK1Ny5cN55sG5dsO+44+Bw1U2T4pLuDNFJzrluzrlR65OhZtYAwDnXO2vRSe6FFVTScnkpBBtv7JOiW24Z7Fu7FoYOhSla2SWVetvMdAVIpBD9+COcc054RfnjjoP+/aOPSaS4aIwUKSZLlsAZZ8CKFcG+/feH006LPiaRLEs3IXpFSNt/MxmI5KHFi+Grryq2mfmK3iKFoGVLv6dot27BvrIyuPhieEITGySlPfEf+Oaa2Qwz+8jMZuQ6KBGpwvqLXosWBfv69dOHOpHM0BgpUixWroSzzoLvvgv29eoFI0eq+KAUpUqXzJtZW6A90MjMdgAs0dUM0A70xS5suXzXrtC8efSxiNRUs2Zw661+kE8uqOSc3xh81Sr4619zE5/kswNyHYCI1MB114UX0OvUCa64Qh/qRDJDY6RIMSgrgxEj4JNPgn0dO/r9tuvXjzwskShUtYfofvhCSpsCY8u1LwcuzFJMki+0XF6KxQYbwE03wbnnwttvB/uvv95fGR0wwM+Cllgzszb4MW5L4CNglHNuWW6jEpG0PPEEPPposL1ZM1WUF8kAjZEiReaGG+CNN4LtLVv6z0/NmkUekkhUKr1E7py7xzm3J3C8c27PcreDnXNaZ1rMnFNCVIpLw4YwdizssUd4/223wc03+//7Enf3AiuAm4Em+Eq6IpLvpk+Ha64JtpeUwNVXQ/v2kYckUoQ0RooUi0cfhQcfDLbXr+8/N7VrF31MIhGqasn8/znn7gc6mtnZyf3OubEhd5Ni8NVXfmPl8urWhZ49cxKOSEbUrw+jR8Mll8Dzzwf7773XL58/7zwtqYy3ts654YmvXzCzkLW3IpJXFi+G88/3+4cmO+cc6KPaLyIZojFSpBi89RZce22w3cxvL7PddtHHJBKxqpbMb5D4t0m2A5E8EzY7tHt3aNQo+lhEMqluXbjsMj9j9Kmngv2PPuqXz48cCXXqRB6e5AUzsw35bd/sOuW/d84tzVlkIhJUWuovZC0N+dU85BA48sjoYxIpXhojRQrd3LkwbJjfPzTZ6afDXntFH5NIDlSaEHXO3Zb499JowpG8EVZQSbMrpFiUlMDw4X4vubBlIv/8J6xe7a+O1qsXfXySa82B9/jtwx7A+hkwDugUeUQiEs45GDUKZs0K9nXv7qvNa29okUzSGClSyJYuhSFD/ASQZIceCn/7W+QhieRKVTNEATCza4ArgFXA80APYEhiOb0Um7IymDYt2K79Q6WYmPnK840awR13BPv/9S+fFL3mGmjQIPr4JGeccx1zHYOIpOnRR+GZZ4LtrVv7v9+qjCuSURojRQpYaakvMrtoUbCvb19dRJTYSXeTvH0T1QMPBBYAXYHzshaV5NYnn8Dy5RXbGjeGbbfNTTwi2WIGp57ql4aEefNNOPPM8CuoIiKSWx98ANddF2yvV88nQ1u1ij4mERGRfOQcXH45zJgR7NtiC198sG5a8+VEika6CdH1a0b7Aw9pb5giF7Zcfocd9AdSitdxx/liHGGmTYPTTgteJBARkdxZvNjPZFm3Ltg3bBhsv330MYmIiOSru+6C554LtjdvDjfcAE2bRh6SSK6lmxB9xsw+AXoD/zKz1sDq7IUlORVWUEnL5aXYHXkkXHxxeHX5jz6Ck0+GH3+MPi4REamotNQnQ8OKKB1+uC+kJCIiIt4rr8AttwTb69XzKy3at48+JpE8kFZC1Dk3DNgF6O2cWwOsAPRusxiVlvolaMlUUEni4KCD4Morw6vLf/YZDBzoZyVJbJjZbmZ2QuLr1ma2Ra5jEom9667zF6qS9egB55wTfTwiMaUxUqQAfPopjBwZ3jd8OPTsGWk4Ivkk3RmiANsAfzGzY4HDgX2zE5Lk1IwZPila3oYbwpZb5iYekaj94Q8wZkx4IY4vvoCTToKFC6OPSyJnZhcDQ4ELEk31ABUTFMmlyZPh8ceD7Rtt5Pc/q1cv2CciGacxUqQA/PADnH22LxSb7Ljj4MADo49JJI+klRA1s/uAMcBuQJ/ErXcW45JcCVsu36dP+DJikWK1++5+L52GDYN933wDAwbAV19FHpZE7lDgYPyqCJxzCwFtsCSSK598AqNHB9vr1FERJZHoaYwUyWelpXDeefDdd8G+fv18jQSRmEu3Sk5voJtzzmUzGMkDYQWVtFxe4qhvXxg/Hs44A1asqNi3eLGfKTp+PHTpkpv4JAqlzjlnZg7AzDbIdUAisbVsmS9+l7yKBeDcc/1yeRGJksZIkXzlHIwaFV5Rfsst4YorNOFJhPSXzM8E2mYzEMkDK1bArFnBdhVUkrjq0QNuu81XX0y2dKkvtDR7dvRxSVQeMbPbgBZmdhLwMnB7jmMSiZ+yMhgxIny7kgMP9IWURCRqGiNF8tVDD8EzzwTbW7SAsWOhcePIQxLJR+kmRFsBs83sBTObvP6WzcAkB957z3/oKK9dO1Wdk3jbemu4/Xa/P12yZcvglFPg/fejj0uyzjk3BngMeBzYChjpnLs5t1GJxNCkSfDWW8H2rl3hggvALPqYRGJOY6RInnr7bb/1V7K6deHaa/3nexEB0l8yf0k2g5A8oeXyIuE6dfIfyE89Fb79tmLfypVw+um+ENMuu+QmPskKMzsLeNQ591KuYxGJrbfe8helkjVt6j/YNWgQfUwiojFSJB99/bW/UJg8yQlg2DDYYYfoYxLJY2nNEHXOvQ58CdRLfD0V0JSoYvPOO8G2nXaKPg6RfLTZZj4putlmwb5ff/UVHF97LfKwJKuaAS+Y2b/N7DQz2zjXAYnEyqJFfql82Bb2l1+uFSwiuaUxUiSfrFjhP48sXx7sO+oo+NOfIg9JJN+lW2X+JPySiNsSTe2Bp7IUk+TCDz/AvHnB9t69o49FJF+1betnKnXqFOxbs8YX/Hjhhejjkqxwzl3qnNsWOA1oB7xuZi/nOCyReCgt9bNZli0L9g0YALvtFn1MIvI/GiNF8khZGYwcCV98Eezr2xfOOiv6mEQKQLp7iJ4G/A5YBuCc+xxoU9kdzKyhmb1rZh+a2Swzu7R2oUpWhS2X33JLaNky+lhE8lmrVj4pus02wb71hT+eeirysCSrFgPfAj9QxdgnIhlyww3hhR533hkGDow8HBFJSWOkSK5NmgSvvx5sb9/eV5uvUyf6mEQKQLoJ0V+dc6XrvzGzukDI+qWK9wH2cs71AHoC+5vZzjWKUrLv3XeDbaouLxKueXO49Vbo2TPY5xxccQU8+GDkYUlmmdmpZvYa8C98ccGTnHPdcxuVSAy8+CI88kiwfeON/d/XknTfvopItmiMFMkTr70GEycG2xs18hXlmzePPCSRQpFuUaXXzexCoJGZ/QEYBDxT2R2ccw74JfFtvcStqiSq5IJz4QlRFVQSSa1JE7j5ZjjnnPDfn7FjYfVqOPHE6GOTTNkcGOKcm57rQERi44sv/P6gyerWhdGjoUWLyEMSkVAaI0Vy7Ysv/FL5MJdeCp07RxuPSIFJ9xL7MGAJ8BFwMjAFGFHVncysjplNxy+leMk5F1K1R3JuwYJg5eySEujVKzfxiBSKRo38ss5+/cL7b7kFxo0LLwgiecvMmiW+vAaYb2Yty99yGZtIUVu1CoYO9f8mO+ss2H776GMSkQo0RorkiV9+8RMzVq4M9g0YAHvtFX1MIgUmrRmizrkyM3sKeMo5tyTdB3fOrQN6mlkL4Ekz2845N7P8MWY2EBgI0KFDh3QfWjIpbP/Q7baDDTaIPhaRQlO/Plxzjb86++KLwf677/ZvVM49V8s8C8eDwIHAe/iVDVauzwEhVbVEpNauuSa8wOMf/gBHHhl9PCISRmOkSK6tL6I0f36wb/fdtde2SJoqTYiamQEXA4Pxg52Z2TrgZufcZek+iXPup8QeM/sDM5P6JgITAXr37q1pVLmg/UNFaqduXb+vXcOGMHlysP+RR/zy+REjlBQtAM65AxP/bpHrWERiY/JkeCZkN6YOHeCii8As2CcikdMYKZIH7rgD3ngj2L755n7bGX3eEElLVb8pQ/DV5fs45zZyzrUEdgJ+Z2ZnVXZHM2udmBmKmTUC9gE+qXXEklllZeEzRJUQFamekhKf8DzqqPD+yZN9/9q10cYlNWZm/0qnTURqae5cuPrqYHuDBn7WaOPG0cckIpXSGCmSI//5T3gRpcaN4brrfJ0DEUlLVUvmjwX+4Jz7fn2Dc26emf0f8CJwfSX33QS4x8zq4BOvjzjnnq1twJJhc+bAzz9XbGvQwC+ZF5HqKSnxe/k0agR33RXsf/FFP1N09Gi/1F7ykpk1BBoDrcxsQ35bDtgMaJezwESK0cqVft/QX38N9g0dCltuGX1MIpKSxkiRHPr6a79qIqw+wWWXQceOkYckUsiqSojWK58MXc85t8TM6lV2R+fcDGCH2gQnEQhbLr/DDkrWiNSUGZx2mk+K3nJLsP+NN2DIEBgzRrOe8tfJ+BUS7fB7pK3/sLcMGJ+jmESKj3P+AtGXXwb7DjwQDj448pBEpEoaI0VyYdUqOO88WL482Pf3v8Mee0Qekkihq2rJfGkN+6RQaP9Qkew48UQ/WzTMu+/C4MG+OqTkHefcjYm90c51znVyzm2RuPVwzo3LdXwiReOZZ2DKlGB7p05+dqiI5B2NkSI54BxceaVf3Zls113h5JOjj0mkCFQ1Q7SHmS0LaTegYRbikSitWQPvvx9sV0JUJDOOPtrPAr3iiuDSlhkz4JRTYNw4aNEiJ+FJ5ZxzN5vZdkA3yo15zrl7cxeVSJGYNy9839CGDX17o0bRxyQiadMYKRKhRx6B558Ptrdr5z9nqIiSSI1U+pvjnKvjnGsWcmvqnKt0ybwUgJkz/X6G5TVrBl275iYekWJ0yCGp36h88gkMHAjfB3YmkTxgZhcDNyduewLXAGmt4TWz/c3sUzObY2bDKjmuj5mtM7PDMxK0SCFYtQqGDQvfN/TCC2ELFa8WyXe1GSNFpBpmzICxY4Pt9ev7LbiaNYs+JpEioUsJcRZWXb53b11hEsm0/faDa6+FeiHXkebNgwEDYNGi6OOSqhwO7A1865w7AegBNKjqToliguOBA/AzZ442s24pjrsaeCGTQYvkvWuv9X/7kh10EPTvH308IlITNRojRaQali71W8isWxfsGzFCE5lEakmZrzjT/qEi0fn97+HGG/1y0GQLFvik6Pz50ccllVnlnCsD1ppZM2Ax0CmN+/UF5jjn5jnnSoGHgUNCjjsdeDzxuCLx8NxzMHlysH2LLeD886OPR0RqqqZjpIikY906v2piyZJg35FH6gKiSAYoIRpXK1fCRx8F25UQFcmevn39nqEbbBDs++47nxSdOzf6uCSVaWbWArgdX0n3fSDkSlJAe+Drct8vSLT9j5m1Bw4FJmQkUpFC8PXXMGpUsL1BA19tXvuGihSSmo6RIpKOW2+FadOC7dtvD2edFX08IkVICdG4+uCD4NT7jTeGzTbLTTwicdGzp3+DE7bfz9KlcNJJ8PHHkYclQc65Qc65n5xzE4A/AMcllgVWxcIeLun7G4ChzrmQNVDlHshsoJlNM7NpS8JmCIgUitJSuOACf0E22fnnQ+fO0cckIjVWizFSRKryxhtw993B9g039IUHw7bhEpFqU0I0rlItl7ewz/EiklHdusHtt0PLlsG+Zct89fnp0yMPSzwz65V8A1oCdRNfV2UBUP7q0qbAwqRjegMPm9mX+H3YbjGzPyU/kHNuonOut3Oud+vWrWtyOiL5Ydw4X0gu2X77wcGqwyJSKDIwRqrwoEhlvvkGLr442F5SAldeCW3aRB+TSJGqm+sAJEfCCir16RN9HCJx1bkzTJoEp57ql8uXt2IFDB4M110HO+2Um/ji7bpK+hywVxX3nwp0MbMtgG+Ao4BjKjyIc/8ro21mdwPPOueeqkmwInnvP/+BBx8Mtrdv7/dH08VYkUJSqzGyXOHBP+AvIE41s8nOudkhx6nwoMRLaakvorR8ebDvlFO0vZ1IhikhGkc//giffRZsV0JUJFodOvyWFF2woGLf6tUwZIhfFtOvX07Ciyvn3J61vP9aMxuM/xBXB7jTOTfLzE5J9GvfUImPJUvgkkuC7XXr+v1Ew/ZUFpG8VdsxknKFBwHMbH3hwdlJx60vPKgPKBIf110Xvppi993h+OMjD0ek2CkhGkdhs0O32AK0HFMkepts4pOigwbBvHkV+9asgXPPhSuugH33zU18MWZmx4a1O+fureq+zrkpwJSkttBEqHPu+JrEJ5L3ysr8sr+ffgr2DR7stw8RkYJUizEyrPBgheUw5QoP7kUlCVEzGwgMBOjQoUPVQYvks+eeg8cfD7a3aweXXuqXzItIRum3Ko7CEqKafi+SO61awcSJsNVWwb6yMhg+HJ5+Ovq4pE+52+7AJYA2OxRJ1333he9ZvuuucMwxwXYRKSQ1HSMzVnhQ+2xL0Zg3z+8PmqxePRg9OrwYq4jUmmaIxlGqgkoikjstWsCECXDmmTBjRsU+5+Dyy2HVKjjqqJyEF0fOudPLf29mzYH7chSOSGGZNQtuuSXYvtFGfgm9ZrqIFLRajJHVKTwI0Arob2Zrtde2FKVVq2DYML9dVrJzztFqCpEs0rvRuFm40FeuK6+kBHqlVRRSRLKpaVNfiTnVfr5jxsBdd0Ubk5S3EuiS6yBE8t7KlX5m+7qQyV2XXQYtW0Yfk4hkW7pj5P8KD5pZfXzhwcnlD3DObeGc6+ic6wg8BgxSMlSKknN+BmjytlkA++0Hf/5z9DGJxIhmiMZN2HL5bbbxiRgRyb3GjeHGG+H8831l5mTjx/sryaeeqsrMWWZmz/DbMr4SoBvwSO4iEikQo0cHC8UBHHss7LRTsF1ECk5Nx0gVHhQp55ln4J//DLZ37OgvLOq9vkhWKSEaN1ouL5L/6teHa6+FkSPhpZeC/Xfe6WdgnX22lp1m15hyX68FvnLOhWR5ROR/XngBpkwJtnfr5i/kiEixqPEYqcKDIsDcuXD11cH2Bg18e+PG0cckEjNKiMaJc+EzRFMtzxWR3KlXz2+u3rChv3qc7OGH/UzR4cOVFM0S59zrAGbWjMR4aWYtnXNLcxqYSL5auBCuuirY3qgRXHGF/7smIkVBY6RILazfN/TXX4N9w4ZB587RxyQSQ0qIxsncubA06T1K/frQs2dOwhGRKpSUwEUX+WTCIyGr0J5+2r+huuwyqKs/55lmZgOBy4FVQBm+Mq4DOuUyLpG8VFbmZ7WvWBHsGzoUOnSIPiYRyRqNkSK1cPXV8MUXwfaDDvI3EYmEPkHHSdhy+Z49fVJURPJTSQmcd55Pit5zT7D/xRd9VcrRo/W7nHnnAds6577PdSAiee+uu2D69GD7vvvCH/8YeTgiknUaI0Vq4tln/S1Zp06+hoCIREbrLONEy+VFCpMZDB4MgwaF97/xBpx1lp8tKpk0F181V0QqM3Mm3HZbsH3jjf3SPxWFEClGGiNFquvLL/0khmQNGvj2Ro0iD0kkzjRDNC7WrYP33gu2q6CSSGEwgxNP9HuKjh0b7H/nHTj9dLjhBmjSJPLwitQFwFtm9g7wv02enHNn5C4kkTyzciWMGOGXzJdXUgKXXw7NmuUmLhHJNo2RItXx66/+IuHq1cG+oUP9DFERiZQSonExa5b/0FJekyawzTa5iUdEauaYY/zV46uu8oXSyps+3VdxHjcOmjfPSXhF5jbgFeAj/P5oIpJs7FhYEFJY+vjjoVevyMMRkchojBSpjrFjYc6cYHv//to3VCRHlBCNi7Dl8jvuqOrUIoXo0EN9UnTkyOCsrI8/hoED4ZZbYKONchNf8VjrnDs710GI5K3XXoOnngq2b7ut/zskIsVMY6RIuv71L3j88WB7hw7aWkYkh5QNi4uwgkpaLi9SuPbfH665BurVC/bNnQsnnQTffht9XMXlVTMbaGabmFnL9bdcByWSF77/3i+JT9awoW+vq2vuIkVOY6RIOhYuDB8v69f3+4Y2bhx9TCICKCEaD6tXw4wZwXYlREUK2x57wPXX+43Yk82fDwMGwNdfRx5WETmGxB5pwHuJ27ScRiSSD5yDyy6Dn38O9p1zjp/xIiLFTmOkSFXWroXhw+GXX4J9Z58NXbtGH5OI/I8SonEwfTqsWVOxrVUr6NgxF9GISCbtvLPfMzTs6vK33/qk6Lx50cdVBJxzW4TctOO9yKOPwltvBdv79YM//SnycEQkehojRdJw223w0UfB9r32gj//Ofp4RKQCrWeKg1TL5bVXiUhx2GEHmDABBg+GZcsq9v3wg18+P348bL11buIrUGZ2bFi7c+7eqGMRyRtffQU33hhsb9kSLrpI7y1EYkJjpEgV3n0X7r472N62LYwYofFSJA9ohmgchBVU6tMn+jhEJHu6dfNXoVuGbN/1889w8snhW2dIZfqUu+0OXAIcnMuARHJq7Vqf9Pz112DfyJGw4YbRxyQiuaIxUiSVH3/046JzFdtLSuCqq6BZs9zEJSIVaIZosVu2DD75JNiu/UNFik+XLnD77XDqqbB4ccW+FStg0CAYO1a//2lyzp1e/nszaw7cl6NwRHLvzjth9uxg+5//DLvtFn08IpIzGiNFUnAOLr3UFx9Mdsop0L179DGJSCjNEC1206YFr0x16AAbb5ybeEQkuzbfHCZNgvbtg32rV8OQIfDvf0ceVpFYCXTJdRAiOTFrlv/bkqxDB/93RUTiTmOkCMAjj8B//hNs790bjj8+8nBEJDUlRIudlsuLxE+7dn6maFjhtNJSOPdceOmlyMMqNGb2jJlNTtyeBT4Fns51XCKRW73aL5UvK6vYXlLiq803apSbuEQkZzRGioT4/PPwfbabN/fjZYnSLyL5REvmi11YQaWddoo+DhGJVps2MHGiL7T02WcV+9atg+HDYdUqOFjbfVViTLmv1wJfOecW5CoYkZy56SaYPz/YfuKJsN120ccjIvlAY6RIeatX+/fXpaXBvosv9u/NRSSvKCFazBYv9tVgyzPz0/VFpPi1bOmrz595Jnz0UcW+sjJ/pXr1ajjyyNzEl6fMbEtgY+fc60ntu5tZA+fc3ByFJhK9d9/1y/+SbbMNDBgQfTwiklMaI0VSuOEGmDcv2H7kkdCvX+ThiEjVNGe7mIXNDt1qK1W1E4mTZs1g/HjYccfw/muugXvuiTam/HcDsDykfVWiTyQefvnFF4ZIVr8+XH451NV1dZEYugGNkSIVvfEGPPZYsL1zZz8xQUTykhKixSwsIarq0iLx07ixX/L6u9+F9998M9x6a7AAW3x1dM7NSG50zk0DOkYfjkiOjBkD330XbD/99PA9ikUkDjRGipT3/fd+1VWy+vXhqqugQYPoYxKRtGQtIWpmm5nZq2b2sZnNMjNdGomScyqoJCK/adDAJzf22iu8/4474PrrlRT1GlbSp+oxEg+vvw7PPhts790b/vKX6OMRkXyhMVJkvbIyuOQS+OmnYN+QIX6GqIjkrWzOEF0LnOOc2wbYGTjNzLpl8fmkvK++giVLKrbVrQs9e+YkHBHJA/XqwahR8Mc/hvc/+KC/kp1cSTp+pprZScmNZvZ34L0cxCMSrR9/hCuvDLY3buwLQ6hKrkicaYwUWe/hh+Htt4Ptu+0GRxwRfTwiUi1Z2/zJObcIWJT4ermZfQy0B2Zn6zmlnLDl8t27QyNduBWJtTp1fEKjUaPwvY6efNIXWrrkEn9sPA0BnjSzv/Lbh7veQH3g0FwFJRIJ5/yFk6VLg33nngubbBJ9TCKST4agMVIE5syBceOC7S1bwsiRvpixiOS1SHbDN7OOwA7AOyF9A4GBAB06dIginHjQ/qEikkpJCQwd6md73XtvsP+553xS9Mor/f5HMeOc+w7Y1cz2BLZLNP/TOfdKDsMSicZLL8ErIf/V+/WDgw6KPh4RySsaI0WA0lIYPtz/m+ySS3xSVETyXtYTombWBHgcGOKcW5bc75ybCEwE6N27tzavy4SyMngvZMWKEqIisp6ZL4zSqBHcdluw/9VX4Zxz4NproWFl24UVL+fcq8CruY5DJDI//ACjRwfbmzf3H/w020VEEjRGSqyNGwdz5wbb//IX2HXX6OMRkRrJ6iZQZlYPnwx9wDn3RDafS8r55BNYvrxiW+PG0E1buIpIOWZw0klw1lnh/f/9L5xxBqxYEW1cIhI95/ys8GWBa9cwbBhstFH0MYmIiOSbd9/1++4n69TJv28WkYKRzSrzBtwBfOycG5ut55EQYcvle/XyRZVERJL99a9w4YXhs7/efx9OPTU8SSIixeOf/4Q33gi277MP/OEP0ccjIiKSb5Yt83vxJ6tXD664Aho0iD4mEamxbM4Q/R3wN2AvM5ueuPXP4vPJeto/VESq67DD4NJLw6tHz54NAweGF1kRkcK3eDGMGRNsb9nSzw4VERGJO+fgqqtgyZJg32mnQdeu0cckIrWSzSrz/wG02VTUSkth+vRguxKiIlKV/v39fqEXXghr11bsmzMHBgyACROgTZvcxCcimeecn9Xyyy/BvgsugBYtIg9JREQk7zz3HLz8crC9d2845pjo4xGRWsvqHqKSAx9+GKx217IldO6cm3hEpLDstReMHRteXX7+fJ8UXbAg+rhEJDuefRbeeivYfsABsOee0ccjIiKSb779Fq6+OtjetGnqFVYikvf0m1tspk4NtvXurcqwIpK+XXeFm2/2xdiSLVzoCzF98UX0cYlIZi1eDNddF2zfaCM477zo4xEREck3ZWVwySXhRUaHDYONN448JBHJDCVEi432DxWRTNhxRxg/3l/5TrZkiU+KfvZZ9HGJSGasryoftlR++HBo1iz6mERERPLNww/DtGnB9v328zcRKVhKiBaT5ct98ZNkSoiKSE1svz3cdhtsuGGw76ef4OST4aOPIg9LRDLg2WfhzTeD7f37Q79+0ccjIiKSb+bNg3Hjgu1t2sDQodHHIyIZpYRoMXn/fT+lv7z27aFdu9zEIyKFr2tXuP12aN062Ld8OQwaFH7VXETyV2VL5c89N/p4RERE8s2aNXDRRcH6HOCX0GslhUjBU0K0mGi5vIhkQ8eOMGlS+MWVVavgjDPCZ5qJSP5xDkaN0lJ5ERGRykyaBJ9+Gmw/6ih9xhYpEkqIFpOwgkp9+kQfh4gUn/bt/RvDzTcP9pWWwjnnwCuvRB+XiFTPCy/Av/8dbD/gAC2VFxERAZg5E+66K9jesSOcfnrk4YhIdighWiy+/97vcZJMCVERyZQ2bfzy+S5dgn1r1/pKm1OmRB+XiKRn6VK45ppge8uWWiovIiICsHo1jBwZ3IqupAQuuwwaNMhNXCKScUqIFouw5fJduoQXQxERqamWLX2hpW23DfaVlfk3kI8/Hn1cIlK1a66BZcuC7cOGQfPm0ccjIiKSb8aNg/nzg+0DBkC3btHHIyJZo4RosQhbLq+9TUQkG5o1g1tvhV69wvtHjYL77os2JhGp3CuvwMsvB9v/8AfYa6/o4xEREck3U6fCww8H27t1gxNPjD4eEckqJUSLgXMqqCQi0WrcGG66CXbdNbz/xhth4kT/90lEcmvZMhg9OtjevDmcd1708YiIiOSbFSvg0kuD7fXr+/a6daOPSUSySgnRYvD11/DddxXb6tSBHXbITTwiEg8NG8KYMbDnnuH9Eyf6xKiSoiK5NXas3z802fnn+20wRERE4m7sWPj222D74MGwxRbRxyMiWaeEaDEIWy6/3XZ+BpeISDbVr+9nnh1wQHj//ff7/uSN6UUkGv/9Lzz7bLC9Xz/Yd9/o4xEREck3b74JTz8dbO/VC446Kvp4RCQSSogWAy2XF5FcqlPHLyU67LDw/scfh0sugXXrIg1LJPZWroQrrwy2N2kCF1wAZtHHJCIikk+WLYPLLw+2N27s37+WKGUiUqz0213oyspUUElEcq+kxCdYjjkmvH/KFN+/Zk20cYnE2fjx4cv/zjoLWreOPh4REZF8M2YMfP99sH3IEGjXLvJwRCQ6SogWus8+81e1ymvY0C+ZFxGJkplPtJx0Unj/K6/AOefAr79GG5dIHH34ITzySLC9Tx84+ODo4xEREck3r7/uL9on23lnOPTQ6OMRkUgpIVrowpbL9+oF9epFH4uIiBmcfDKccUZ4/1tv+b6VK6ONSyROSkv98r/kgmYNGsCIEVoqLyIi8vPP4dvKbLABXHSRxkqRGFBCtNCFLZfv0yf6OEREyjv2WBg6NLzvvfdg0KBo4xGJkzvvhC+/DLafdhq0bx95OCIiInnnmmtg6dJg+7nnwsYbRx+PiEROCdFCtmYNfPBBsF37h4pIPjjiCLj44vDN6GfOjD6eCJnZ/mb2qZnNMbNhIf1/NbMZidtbZtYjF3FKEZozB+66K9i+7baqlCsiIgLw6qvwwgvB9t13hwMPjD4eEckJJUQL2UcfwerVFduaN4cuXXITj4hIsoMOgquu8pXoY8LM6gDjgQOAbsDRZtYt6bAvgN8757oDlwMTo41SilJZmV8qv25dxfY6dWDkSFXKFRER+eknGDUq2N60KVx4oZbKi8SI3hkXsrDl8r176wOPiOSXffaB666D+vVzHUlU+gJznHPznHOlwMPAIeUPcM695Zz7MfHt28CmEccoxegf/4BZs4LtJ5wAnTtHH4+ISAitopCcuvba8KXy550HrVtHH4+I5IwyZ4XsnXeCbVouLyL5aLfd4MYboVGjXEcShfbA1+W+X5BoS+XvwHNZjUiK38KFMH58sL1jRzjxxMjDEREJo1UUklOvvRa+VL5fPzjggMjDEZHcUkK0UK1cGT4LRAlREclXffr4hE2TJrmOJNvC1lq5kDbMbE98QjS0ApWZDTSzaWY2bcmSJRkMUYqKc75SbvI2Oma+Um58ZmeLSP7TKgrJjZ9/9ts4JdNSeZHYUkK0UL3/fnCPsLZtYVO9XxCRPNa9O9x2G7RoketIsmkBsFm57zcFFiYfZGbdgUnAIc65H8IeyDk30TnX2znXu7WWcUkqTz0VvmrkiCOgh1aaikhe0SoKyY3Klsq3ahV9PCKSc0qIFqp33w229e2rK1sikv+22gruvjvXUWTTVKCLmW1hZvWBo4DJ5Q8wsw7AE8DfnHOf5SBGKRbffgvXXx9sb9MGTjst+nhERCqnVRQSvddeg+efD7bvvruWyovEmBKihSqsoFKfPtHHISJSE0U8m905txYYDLwAfAw84pybZWanmNkpicNGAhsBt5jZdDOblqNwpZA556vKr1wZ7BsxAjbYIPqYREQqp1UUEq2lS/22Msm0VF4k9urmOgCpgaVL4fPPg+1KiIqI5AXn3BRgSlLbhHJfDwAGRB2XFJmnnw5fKn/wwbDrrtHHIyJStf+togC+wa+iOKb8AVpFIRnjHIwaBT/+GOxTVXmR2FNCtBBNC5lI1KmT9j4RERGJi2+/hbFjg+1t2sBZZ0Ufj4hIGpxza81s/SqKOsCd61dRJPonUHEVBcBa51zvXMUsBWzKFHj11WC7qsqLCEqIFiYtlxcREYmvsjK49NLUS+WbNo0+JhGRNGkVhURi4UK4+upge/PmMHy4lsqLiPYQLUipCiqJiIhI8XvoofCLo1oqLyIi4i8cjhwZfuHwwgtho42ij0lE8o4SooVm4UL45puKbSUl0KtXbuIRERGR6Hz+OYwbF2zXUnkRERHv7rth+vRg+/77w957Rx2NiOQpJUQLTdjs0G7dtDxORESk2JWW+iXxa9YE+y65RO8FREREPvoIJkwItrdtC0OHRh+PiOQtJUQLjZbLi4iIxNO4cTB3brD9mGP0XkBEROSXX/z+oGVlFdvN4LLLdOFQRCpQQrSQOBdeYV4FlURERIrb22/Dgw8G2zt3hsGDo49HREQknzgHV13lt5hLdtxx2mJORAKylhA1szvNbLGZzczWc8TO3LmwdGnFtvr1oUeP3MQjIiIi2ff993DRRcH2evXgiiv8ewEREZE4e/JJePHFYPu228Ipp0Qfj4jkvWzOEL0b2D+Ljx8/Ycvle/bUByEREZFiVVbm9w398cdg3+DB0KVL9DGJiIjkk88+gzFjgu2NG/tZo3XrRh+TiOS9rCVEnXNvAEurPFDSp/1DRURE4mXSpPDtcvr2haOPjj4eERGRfLJiBQwb5gsPJhs+HNq3jz4mESkI2kO0UKxdC++/H2xXQlRERKQ4TZsGt98ebG/Z0i+VL9HbOBERiTHn4NJLYf78YN+hh8J++0Ufk4gUjJy/kzazgWY2zcymLVmyJNfh5K/Zs2HlyoptTZvC1lvnJh4RERHJnh9+8EvlnavYbuaToS1b5iYuERGRfPHAA/DKK8H2LbeEc8+NPh4RKSg5T4g65yY653o753q3bt061+Hkr7Dl8jvuqNkhIiIixWbtWhg61BdTSjZggFaHiIiIvPce3HRTsL1xYxg9Gho0iD4mESkoyqYVCu0fKiIiEg/XXw/Tpwfbe/WCk06KPBwREZG8smiRv3BYVhbsGzkSOnaMPCQRKTxZS4ia2UPAf4GtzGyBmf09W89V9Fatghkzgu1KiIqIiBSXKVPgH/8ItmvfUBEREfj1VzjvPPjpp2DfMcfAPvtEHpKIFKa62Xpg55xKn2bK9Ol++Vx5rVvD5pvnJBwRERHJgk8/9UnPZCUlfvlfmzbRxyQiIpIv1hdR+uSTYN8OO8AZZ0Qfk4gULE0zKARTpwbb+vTxhRVERESk8C1d6gtAlJYG+4YM8cvlRURE4uyOO+DFF4PtbdrA1VdD3azN9xKRIqSEaCHQ/qEiIiLFq7TUJ0MXLQr27b8/HK1FNyIiEnOvvAITJgTb69eHMWP81jIiItWghGi++/lnv4QumRKiIiIihc85uPzy8L3Cu3SBESO0IkREROJt5kw/HoYZMQK6dYs2HhEpCkqI5rtp0/yHpfI231z7iImIiBSDO++E554Ltjdr5me8NGwYfUwiIiL54ptv4KyzwreUOeEE6N8/+phEpCgoIZrvtFxeRESkOL30Etx6a7C9bl2fDG3fPvqYRERE8sWyZb5Q0o8/Bvv22ANOPTXykESkeCghmu9SFVQSERGRwvXeezByZHjf8OEqoiQiIvG2erUvKvjVV8G+rbeGyy6DEqUzRKTm9Bckn333HcyfX7HNDHr3zk08IiIiUnuffQZnnw1r1gT7jjsODjoo+phERETyxdq1MHRo+P7aG28MN9wAjRtHHpaIFBclRPNZ2HL5rbf2+4qJiIhI4Vm4EE4/HVasCPbtsQecdlrkIYmIiOSNsjJfbPDNN4N9G2wAN90ErVpFH5eIFB0lRPNZWEJUy+VFREQK048/wuDB8MMPwb7tt/cfALX8T0RE4so5uPZa+Oc/g3316sF110HnztHHJSJFSe+685Vz4QnRnXaKPhYRERGpnWXLfDI0eSscgI4d/fK/Ro2ijkpERCQ/OAc33wyPPhrsM4Mrr9TWcSKSUUqI5qsvvgjOIKlXD3r0yE08IiIiUjMrVvhl8p9+Guxr3RrGjYPmzaOPS0REJF/cfjvce29437BhsNde0cYjIkWvbq4DkBTCqst37w4NG0Yfi4iIiNTMypU+GTprVrCvaVOfDG3bNvq4RERE8oFzMHGiT4iGOe00+POfo41JRGJBCdF8FbZcvm/f6OMQERGRmlm9Gs46K7xKbsOGcP312gtNRETiyzm49Va4887w/hNPhBNOiDYmEYkNJUTz0bp18N57wXYVVBIRESkMv/wCQ4bA9OnBvvr1fTK0Z8+IgxIREckT6/cMTbVM/uij4dRTo41JRGJFCdF89PHH/oNUeY0bw7bb5iYeERERSd/PP/sCSh9/HOxbXyVXFzlFRCSuysrgqqvgqafC+//yFzj7bF9MSUQkS5QQzUdhy+V794Y6daKPRURERNL3/fcwaBDMmxfsq1MHrr4adtkl+rhERETyQWkpjBwJL78c3n/00UqGikgklBDNR2EFlTSTREREJL8tWOBnhi5YEOyrWxdGjYJ+/aKPS0REJB/88gucf374BCCAY47xe28rGSoiEVBCNN/8+it8+GGwXQWVRERE8tdHH/kPcT/9FOxr0ADGjNHMUBERia9Fi+DMM8NXUAAMGAAnn6xkqIhERgnRfPPhh34ZQXktW0KnTrmJR0RERCr3yiswYkRw/Aa/B/gNN0CvXpGHJSIikhdmz/YXDX/4Ibz/7LP97FARkQgpIZpvwpYP9OmjK2UiIiL5xjl48EGf8HQu2N+sGYwbB926RR6aiIhIXnjhBbjsMr8SMllJCVx0ERx0UPRxiUjsKSGab8ISolouLyIikl9Wr/YVcqdMCe/fZBO48Uat8BARkXhatw5uugkeeCC8v3FjGD0adt012rhERBKUEM0ny5fDJ58E25UQFRERyR/ffAPnnQeffRbev802ftboRhtFGpaIiEhe+PFHuOACmDYtvL9NGz9Odu0aaVgiIuWV5DoAKee996CsrGLbppv6WSYiIiKSe2+9BX/7W+pkaL9+MHGikqEiIhJP774LRx+dOhnatSvcfbeSoSKSc5ohmk+0XF5ERCQ/lZb6/UAffDD1MUcd5QtDlOh6s4iIxMyaNXDrrXDvvamP2Xdfv2doo0bRxSUikoISovlk6tRgW58+0cchIiIiv5k7F4YPhzlzwvvr1/f9f/xjtHGJiIjkgy+/9InOjz8O7y8pgdNPh//7PxULFpG8oYRovliyBL74Itjeu3f0sYiIiIgvCPHAAzBhgp8hGqZdO7j2Wthqq2hjExERybU1a+Cee+COO/zXYZo3h1GjtPJRRPKOEqL5Imx2aNeusOGG0cciIiISd7NnwxVXpN4rFGCXXfwxzZtHF5eIiEg++PBDuPJKmDcv9TF9+sCll/oiSiIieUYJ0XwRtn+olsuLiIhE65dffFGkhx8OFjpcr149v/TvqKO0X6iIiMTL0qV+5cQTT6Q+pk4dGDTIFyHUOCkieUoJ0XzgXHhCdKedoo9FREQkjtau9R/uJk6En35KfVynTn5WqKrjiohInKxYAfff72+rVqU+brPN/MzRbt2ii01EpAaUEM0HX38NixdXbKtTB3r2zEk4IiIisVFWBq+95ivIz5+f+jgzPyN08GBo0CCy8ERERHKqtBQeewzuvLPyC4YlJXDssTBgADRsGFl4IiI1pYRoPnjuuWDb9ttD48bRxyIiIhIH69bBCy/A3XdXvv8Z+Nmgw4fDtttGEpqIiEjOLVsGzz4LDz0EixZVfmy3bjBihFZPiEhBUUI013780VewTaYqfCIiIpm3bBlMmQIPPggLF1Z+bP36cMopcMwxUFdvmUREpMg5B7NmweOP+4uGpaWVH9+4sd8r9MgjtVeoiBQcvbvPtbvvhpUrK7bVrQsHHZSTcERERIqOczB9Ojz5JLz8ctUf8AD69/cf8tq2zXp4IiIiObVqFTz/vF8a/+mnVR9frx4cfjiceCJsuGH24xMRyQIlRHNp8WJ49NFg+5//DJtsEn08IiIixWLdOp8EffVVv0fot9+md7/evWHIENh66ywGJyIikiM//wxz5lS8ff45rF5d9X3N/AXDk0+Gdu2yH6uISBYpIZpLt98enKXSsKG/0iYiIiLpW7fOz2r54AN/e/99vzw+Xb16wQknwM47+w98IiIihWz1avjii2Dy84cfavZ4/fr5lRNbbpnZOEVEciSrCVEz2x+4EagDTHLOja70DmvXwpIl2QwpfyxeDE8/HWw/+mjYaKPo4xERkYypavwzM0v09wdWAsc7596v9EHjNEau55y/lZX525o1fmbLTz/5Pbi//dZ/2PvyS18hfs2a6j/Hbrv5RGiPHpmOXkREQmRljIyzsjJYsCCY+FywwPfVRrNmcOCBfgXj5ptnJl4RkTyRtYSomdUBxgN/ABYAU81ssnNudso7ff45HHBAtkLKf02bwt/+lusoRESkFtIc/w4AuiRuOwG3Jv5NLe5jZCat/4D3pz9Bp065jkZEJDayNkbG0bRpcMMNMG9eentjV8e22/o9QvfdFxo0yOxji4jkiWzOEO0LzHHOzQMws4eBQ4DUCdG4O/ZY/yFNREQKWTrj3yHAvc45B7xtZi3MbBPn3KLow42JOnVgxx3h4INhr718BXkREYmaxshMqVcPPvkkc4/XpAnss49PhGofbRGJgWwmRNsDX5f7fgEhV/bMbCAwEKBHnD+ctGwJRx2V6yhERKT20hn/wo5pD1T4sKcxspYaNoRddoE99/RL43XRUUQk17IyRnbo0CHjgea9zp1rdr86dfzy9y23rHhr2xZKSjIbo4hIHstmQjSsIoELNDg3EZgI0HuDDQL9sXHaadCoUa6jEBGR2ktn/NMYmQ0tWkD37tCzJ+ywg5/hUq9erqMSEZHfZGeM7N07fmNkkyY+ifntt6mPadvWJzs7d/4t8bn55lolISJCdhOiC4DNyn2/KbCw8mjqQqtWWQwpD220kV++d8ghuY5EREQyI53xT2NkukpKfrvVqQPNm/vEZ4sWsOGGsNlmsMUW/taiRY6DFRGRKmRnjIyrzp19QrRp0+CMz86dfdJURERCZTMhOhXoYmZbAN8ARwHHVHqPLl3g+eezGJKIiEjWpTP+TQYGJ/ZO2wn4ucq90TRGiohI4cvOGBlX55wDw4dD69ZgYRNrRUQklawlRJ1za81sMPACUAe40zk3K1vPJyIikg9SjX9mdkqifwIwBegPzAFWAifkKl4REZGoaIzMsDjunSoikiHZnCGKc24KfkATERGJjbDxL/Ehb/3XDjgt6rhERERyTWOkiIjkA5WRExERERERERERkdhQQlRERERERERERERiQwlRERERERERERERiQ0lREVERERERERERCQ2lBAVERERERERERGR2FBCVERERERERERERGJDCVERERERERERERGJDSVERUREREREREREJDaUEBUREREREREREZHYMOdcrmP4HzNbDnya6zhypBXwfa6DyKE4n3+czx3iff5xPneArZxzTXMdRKGI+RgJ8f59ifO5Q7zPP87nDvE+f42R1aAxMta/K3E+d9D5x/n843zukIFxsm6mIsmQT51zvXMdRC6Y2bS4njvE+/zjfO4Q7/OP87mDP/9cx1BgYjtGQrx/X+J87hDv84/zuUO8z19jZLVpjIzp+cf53EHnH+fzj/O5Q2bGSS2ZFxERERERERERkdhQQlRERERERERERERiI98SohNzHUAOxfncId7nH+dzh3iff5zPHXT+1RX3n1eczz/O5w7xPv84nzvE+/zjfO41EfefV5zPP87nDjr/OJ9/nM8dMnD+eVVUSURERERERERERCSb8m2GqIiIiIiIiIiIiEjWRJIQNbP9zexTM5tjZsNC+s3Mbkr0zzCzXunetxDU8vy/NLOPzGx6IVabTOPctzaz/5rZr2Z2bnXuWwhqef7F/tr/NfH/fYaZvWVmPdK9byGo5fkX+2t/SOK8p5vZNDPbLd37FiONkRojNUbGb4yEeI+TcR4jQeNkdcV5nIzzGAnxHic1RmqM1BgZwRjpnMvqDagDzAU6AfWBD4FuScf0B54DDNgZeCfd++b7rTbnn+j7EmiV6/PI4rm3AfoAVwLnVue++X6rzfnH5LXfFdgw8fUBMfy9Dz3/mLz2Tfhty5buwCfF8tpn6eelMVJjpMbIIhojq3H+RTlO1ubcY/Taa5ys3s+rKMfJ2px7oi8OvytFOU7W5txj9NprjHQaI6nlGBnFDNG+wBzn3DznXCnwMHBI0jGHAPc6722ghZltkuZ9811tzr/QVXnuzrnFzrmpwJrq3rcA1Ob8C1065/6Wc+7HxLdvA5ume98CUJvzL3TpnPsvLjFqARsALt37FiGNkRojNUbGb4yEeI+TcR4jQeNkdcV5nIzzGAnxHic1RmqM1BgZwRgZRUK0PfB1ue8XJNrSOSad++a72pw/+Bf3RTN7z8wGZi3K7KjN6xeX174ycXrt/46/ul2T++aj2pw/xOC1N7NDzewT4J/AidW5b5HRGKkxcj2NkfEZIyHe42Scx0jQOFldcR4n4zxGQrzHSY2RGiPX0xiZxTGybq1CTY+FtLk0j0nnvvmuNucP8Dvn3EIzawO8ZGafOOfeyGiE2VOb1y8ur31lYvHam9me+D/k6/f+iNVrH3L+EIPX3jn3JPCkmfUDLgf2Sfe+RUZjZJDGyOzeN1/EeYyEeI+TcR4jQeNkdcV5nIzzGAnxHic1RgZpjEw+UGNkrcfIKGaILgA2K/f9psDCNI9J5775rjbnj3Nu/b+LgSfx04ALRW1ev7i89inF4bU3s+7AJOAQ59wP1blvnqvN+cfitV8vMUB3NrNW1b1vkdAYqTFyPY2R8RkjId7jZJzHSNA4WV1xHifjPEZCvMdJjZEaI9fTGJnNMdJlf1PUusA8YAt+29h026Rj/kjFzaDfTfe++X6r5flvADQt9/VbwP65PqdMnnu5Yy+h4kbYsXjtKzn/on/tgQ7AHGDXmv7c8vVWy/OPw2u/Jb9thN0L+Cbx96/gX/ss/bw0RmqMTB4jYvHaV3L+Bf3ap3v+lYwTBf361/Lc4/Laa5ys3s+rKMfJWp57LH5Xyh2bPE4U/WtfybnH4rWvZJwo+te+knOPy2ufsTEyqpPqD3yGr/g0PNF2CnBK4msDxif6PwJ6V3bfQrvV9Pzx1bE+TNxmFeL5p3HubfGZ/GXAT4mvm8XotQ89/5i89pOAH4Hpidu0yu5baLeann9MXvuhiXObDvwX2K2YXvss/Lw0RmqM1BhZZGNkmudftONkTc89Rq+9xsnq/byKdpys6bnH6HelaMfJmp57jF57jZEaI6dTyzFyfVZVREREREREREREpOhFsYeoiIiIiIiIiIiISF5QQlRERERERERERERiQwlRERERERERERERiQ0lREVERERERERERCQ2lBAVERERERERERGR2FBCVKSWzOw1M9svqW2Imd1SyfG9o4lOREQkdzRGioiIpKZxUiR3lBAVqb2HgKOS2o5KtIuIiMSZxkgREZHUNE6K5IgSoiK19xhwoJk1ADCzjkA74Bgzm2Zms8zs0rA7mtkv5b4+3MzuTnzd2sweN7OpidvvEu2/N7PpidsHZtY0y+cmIiJSGxojRUREUtM4KZIjdXMdgEihc879YGbvAvsDT+Ov6P0DGOWcW2pmdYB/mVl359yMNB/2RuB659x/zKwD8AKwDXAucJpz7k0zawKszvgJiYiIZIjGSBERkdQ0TorkjmaIimRG+aUO65c4HGlm7wMfANsC3arxePsA48xsOjAZaJa4gvcmMNbMzgBaOOfWZih+ERGRbNEYKSIikprGSZEcUEJUJDOeAvY2s15AI+BH/BW4vZ1z3YF/Ag1D7ufKfV2+vwTYxTnXM3Fr75xb7pwbDQxIPMfbZrZ1Fs5FREQkk55CY6SIiEgqT6FxUiRySoiKZIBz7hfgNeBO/BW9ZsAK4Gcz2xg4IMVdvzOzbcysBDi0XPuLwOD135hZz8S/nZ1zHznnrgamARrEREQkr2mMFBERSU3jpEhuKCEqkjkPAT2Ah51zH+KXN8zCD2xvprjPMOBZ4BVgUbn2M4DeZjbDzGYDpyTah5jZTDP7EFgFPJf50xAREck4jZEiIiKpaZwUiZg556o+SkRERERERERERKQIaIaoiIiIiIiIiIiIxIYSoiIiIiIiIiIiIhIbSoiKiIiIiIiIiIhIbCghKiIiIiIiIiIiIrGhhKiIiIiIiIiIiIjEhhKiIiIiIiIiIiIiEhtKiIqIiIiIiIiIiEhsKCEqIiIiIiIiIiIisfH/9xlwa0lspuAAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.stats import triang as my_dist                                    # import traingular dist as my_dist\n",
    "dist_type = 'Triangular'                                                     # give the name of the distribution for labels\n",
    "low = 0.05; mode = 0.20; c = 0.10                                            # given the distribution parameters\n",
    "\n",
    "x_values = np.linspace(0.0,0.3,100)                                          # get an array of x values\n",
    "p_values = my_dist.pdf(x_values, loc = low, c = mode, scale = interval)      # calculate density for each x value\n",
    "P_values = my_dist.cdf(x_values, loc = low, c = mode, scale = interval)      # calculate cumulative probablity for each x value\n",
    "\n",
    "plt.subplot(1,3,1)                                                           # plot the resulting PDF\n",
    "plt.plot(x_values, p_values,'r-', lw=5, alpha=0.8); plt.title('Sampling the ' + str(dist_type) + ' PDF, $f_x(x)$'); plt.xlabel('Values'); plt.ylabel('Density')\n",
    "plt.xlim([0.0,0.3])\n",
    "\n",
    "plt.subplot(1,3,2)                                                           # plot the resulting CDF\n",
    "plt.plot(x_values, P_values,'r-', lw=5, alpha=0.8); plt.title('Sampling the ' + str(dist_type) + ' CDF, $F_x(x)$'); plt.xlabel('Values'); plt.ylabel('Cumulative Probability')\n",
    "plt.xlim([0.0,0.3])\n",
    "\n",
    "p_values = np.linspace(0.00001,0.99999,100)                                 # get an array of p-values\n",
    "x_values = my_dist.ppf(p_values, loc = low, c = mode, scale = interval)      # apply inverse to get x values from p-values\n",
    "plt.subplot(1,3,3)\n",
    "plt.plot(x_values, p_values,'r-', lw=5, alpha=0.8, label='uniform pdf')\n",
    "plt.xlim([0.0,0.3])\n",
    "\n",
    "plt.subplots_adjust(left=0.0, bottom=0.0, right=3.0, top=1.1, wspace=0.2, hspace=0.3); plt.title('Sampling Inverse the ' + str(dist_type) + ' CDF, $F^{-1}_x(x)$'); plt.xlabel('Values'); plt.ylabel('Cumulative Probability')\n",
    "\n",
    "print('The mean is ' + str(round(my_dist.mean(loc = low,c = mode, scale = interval),4)) + '.') # calculate stats and symmetric interval\n",
    "print('The variance is ' + str(round(my_dist.var(loc = low, c = mode, scale = interval),4)) + '.')\n",
    "print('The interval at an alpha level of ' + str(round(1-level,3)) + ' is ' + str(np.round(my_dist.interval(alpha = level,loc = low,c = mode,scale = interval),2)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The missing lower tail for the inverse is due to any value less than 0.05 having 0.0 cumulative probability.\n",
    "\n",
    "#### Gaussian Distribution\n",
    "\n",
    "Let's now use the Gaussian parametric distribution.\n",
    "\n",
    "* we will need the parameters mean and the variance\n",
    "\n",
    "We will apply the forward and reverse operations and calculate the summary statistics.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The mean is 0.15.\n",
      "The variance is 0.0025.\n",
      "The interval at an alpha level of 0.05 is [0.05 0.25]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.stats import norm as my_dist                                      # import traingular dist as my_dist\n",
    "dist_type = 'Gaussian'                                                       # give the name of the distribution for labels\n",
    "mean = 0.15; stdev = 0.05                                                    # given the distribution parameters\n",
    "\n",
    "x_values = np.linspace(0.0,0.3,100)                                          # get an array of x values\n",
    "p_values = my_dist.pdf(x_values, loc = mean, scale = stdev)                  # calculate density for each x value\n",
    "P_values = my_dist.cdf(x_values, loc = mean, scale = stdev)                  # calculate cumulative probablity for each x value\n",
    "\n",
    "plt.subplot(1,3,1)                                                           # plot the resulting PDF\n",
    "plt.plot(x_values, p_values,'r-', lw=5, alpha=0.8); plt.title('Sampling the ' + str(dist_type) + ' PDF, $f_x(x)$'); plt.xlabel('Values'); plt.ylabel('Density')\n",
    "plt.xlim([0.0,0.3])\n",
    "\n",
    "plt.subplot(1,3,2)                                                           # plot the resulting CDF\n",
    "plt.plot(x_values, P_values,'r-', lw=5, alpha=0.8); plt.title('Sampling the ' + str(dist_type) + ' CDF, $F_x(x)$'); plt.xlabel('Values'); plt.ylabel('Cumulative Probability')\n",
    "plt.xlim([0.0,0.3])\n",
    "\n",
    "p_values = np.linspace(0.00001,0.99999,100)                                  # get an array of p-values\n",
    "x_values = my_dist.ppf(p_values, loc = mean, scale = stdev)                  # apply inverse to get x values from p-values\n",
    "plt.subplot(1,3,3)\n",
    "plt.plot(x_values, p_values,'r-', lw=5, alpha=0.8, label='uniform pdf')\n",
    "plt.xlim([0.0,0.3])\n",
    "\n",
    "plt.subplots_adjust(left=0.0, bottom=0.0, right=2.8, top=0.8, wspace=0.2, hspace=0.3); plt.title('Sampling Inverse the ' + str(dist_type) + ' CDF, $F^{-1}_x(x)$'); plt.xlabel('Values'); plt.ylabel('Cumulative Probability')\n",
    "\n",
    "print('The mean is ' + str(round(my_dist.mean(loc = mean, scale = stdev),4)) + '.') # calculate stats and symmetric interval\n",
    "print('The variance is ' + str(round(my_dist.var(loc = mean, scale = stdev),4)) + '.')\n",
    "print('The interval at an alpha level of ' + str(round(1-level,3)) + ' is ' + str(np.round(my_dist.interval(alpha = level,loc = mean,scale = stdev),2)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Log Normal Distribution\n",
    "\n",
    "Now let's check out the log normal distribution.  \n",
    "\n",
    "* We need the parameters $\\mu$ and $\\sigma$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The mean is 0.102.\n",
      "The variance is 0.0004.\n",
      "The interval at alpha level 0.05 is [0.07 0.15]\n"
     ]
    },
    {
     "data": {
      "image/png": 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NEhERaZ7qZPtpxJ+IiIiIiIiIiEgV0uIeIiIiIiIiIiIiVaiqLvXdeeedfejQoWmnISJS02bNmvWGu/dLO49ypDolIlIeVKuap1olIlIeilWrqqrxN3ToUGbOnJl2GiIiNc3MXk47h3KlOiUiUh5Uq5qnWiUiUh6KVat0qa+IiIiIiIiIiEgVUuNPRERERERERESkCqnxJyIiIiIiIiIiUoXU+BMREREREREREalCavyJiIiIiIiIiIhUITX+REREREREREREqlDntBMQ+bfXX4cnnoBXX4U994STTgKztLMSkRplZtcDpwJr3H1EzHYDfgGcDGwEznX32clmKVIDtmyBTZtg8+Zwe//9cKuvD9uaPjY0RG9bt4ZbY2P4urEx9+YetsO2WNPn7uEG2z7Pj8V9bJL/daHbOrJvMST9fNIhqlUi0iGNjaGGNtXThoZtXzfdOhKL2+eyy2DnndM+8pqixp+k6+234fbb4ZFH4Pnnc7c98ghceSV06pRKaiJS824ArgZubGb7ScDemds44LeZjyISxx3eeQfWrIE33oA334R16+Ctt2D9+vA/wfr18O678N57225NjTkRiXMDqlUi5aXppFJ2s6vpJFVHG2nZsWI06ppOeCXpC19Q4y9havxJet58Ez796fAGIM4jj8APfwj/9V8a+SciiXP3x81saAu7nAHc6O4OPG1mfcxsN3d/NZkMRcqQe2jqLVsGL78My5fDihVhNP9rr4WReiJSNKpVIu20eXMYeLJoUTgJ1dootbbGpHn6/iSuZI0/MxtMOPPUH2gErnX3X5hZX+CvwFBgOXCmu78Vc/8TCcPSOwHXufuVpcpVUnL11c03/ZpMngw77ghf+lIyOYmIFG4gsDLr61WZWM6bKTO7ELgQYMiQIYklJ5KId96BOXNg3rzwBur558MIPhEpF6pVIo2N4YTUwoXhtmABLFmSzmg3CQ1SSVQpR/w1AP/h7rPNrBcwy8weAM4FHnL3K83scuBy4JvZdzSzTsCvgUmE4jTDzCa7+6IS5itJevFF+Oc/C9v3T38Kzb9Pfaq0OYmItE3cUOTI5Fjufi1wLcDo0aM1eZZUtvp6mDkTpk4NH5ctSzsjEWmZapXUnk2b4KmnYP780OhbvDjEpDxoxF/iStb4ywwffzXz+QYzW0w4u3QGMDGz25+AR8lr/AFjgSXuvgzAzG7N3E+Nv2rxy1/GTx49ZEi4JCjfVVfBPvvA2LElT01EpECrgMFZXw8CVqeUi0jpbN4MDz8cbs88k/ybp7o62G67cOveHbp1C7euXcOtS5dtHzt33nbr1Cnc6uqin9fVhZtZ7uct3SA+1hTP/pgfj9vWFklPeVILU6ycdlraGSRFtUpqw5Ytodl3773w+OOhdknrzEL9zL917ty2WHYdbu1+u++e9lHXnETm+MvMO3Ew8Aywa9OcEu7+qpntEnOXuCHpsZPQalh6BXrmmfBHOd+ll4ZRfddeG275fv97Nf5EpJxMBi7JnJwaB7yjOZOkariHy3fvvhvuvx82bizO43bvDrvuCv36wU47hduOO0KfPrDDDtCrF/TuDdtvDz17Qo8e4c2EiLSXapVUr8ZGmD07NPsefjgsEFUuOnVqWyOta9e2N9uK8fh1dWl/pyQBJW/8mVlP4A7gUndfb4WdQSxoSDpoWHrFaWyEX/wiGh8wAM48M3x+wQVhgtXbb8/d59ln4bnnYL/9Sp+niNQ8M7uFMEJ9ZzNbBXwX6ALg7tcAU4CTgSXARuCz6WQqUkRbt8JDD4VpNp5/vn2P0aUL7LknDBsWzuoPGQKDB8Nuu4WmXi2MJhNJiGqV1KStW+G+++CGGzo25UT//jB8OOy1Vzgx1VojrdBmW+fOaqhJWSlp48/MuhCafn9x979nwq83rSRlZrsBcas7aEh6tbrnHnjhhWj8kku2ndE3g8suC42+pUtz97vlFvj+90ufp4jUPHc/u5XtDlycUDoipdXQEBbU+tOf4JVX2nbfPfaAgw+GkSPDybmhQ8ObHhEpOdUqqSn19aFW3XgjrG5je6BXr9Dky77ttFNp8hQpM6Vc1deAPwCL3f3nWZsmA+cAV2Y+/iPm7jOAvc1sD+AV4CzgE6XKVRLS2Ai/+100fsABMGlSbqyuDs4+G/7nf3Lj990HX/6y/kiLiIgUy7Rp8LOfwcsvF7Z/794wfjwceSSMHg19+5Y2PxERqW3uYdqJq66CtWsLu0/v3vCBD8Chh4Ym3+DBGnEuNauUp2PHA58G5pvZnEzsW4SG321mdh6wAvgYgJkNAK5z95PdvcHMLgHuAzoB17v7whLmKklYsCD+zMyll8b/ET7pJPjVr+Cdd7bFGhrgjjvgwgtLlqaIiEhNePnl0PCbNq31fXv0gOOPh5NPhoMOCnMXiYiIlNqyZXDllWEuv9Z07w4TJ8IJJ8Bhh4VLb0WkpKv6TiV+rj6AY2P2X02Yf6Lp6ymEOSmkWjz+eDQ2bhwcckj8/t26wUc+Atdfnxu//XY491xN9i0iItIejY3w17+Gk2v19S3vO2JEmIP3mGPCqroiIiJJ2LIlLPj4pz+FutWSQw6Bj340jERXrRKJ0AQskpwnnojGjjuu5ft89KPhj/3Wrdti69aFod6nnlrc/ERERKrd2rXwve/BM8+0vN8RR4STbAcfrEujREQkWStWwLe/DYsWtbzfkUfCZz8b5pgVkWap8SfJWL06ulAHwIQJLd9vl11Cc/C++3LjN98Mp5yiNyMiIiKFeuIJ+O53Yf365vcZNQq+9rUw/66IiEjSpkyBH/0INm1qfp+jj4bPfx722Se5vEQqmBp/koy40X777w/9+rV+37PPjjb+XngBFi/WGxMREZHWuMMtt8D/+3/h8zj9+8NXvhJOtumkmoiIJK2xEa6+OqzY25zBg+Eb3wij0kWkYGr8STLi5vc78sjC7jtiBBx4IMyfnxt/7DE1/kRERFqydSv85CdhftzmfPzj8KUvhUnRRUREkrZxY7i0N+49I4QFpc4/H845R/O8i7RDXdoJSA3YuBFmzYrGC238QVjhN19zhUFERERC/f3qV5tv+u20E/zyl2H0hJp+IiKShvXr4YtfbP693aBBYbHHCy5Q00+kndT4k9J7+mloaMiN9esH++1X+GMcfXQ09uKLYe5AERERybVpU7h0d9q0+O1HHBFW9tXlUiIikpZ168JcfQsWxG8//vgwt/vw4cnmJVJl1PiT0mvuMt+2zCG0666w776FPbaIiEgte/99+I//gGefjd9+5plhvr8+fRJNS0RE5N/eeis0/V58MX77F78IP/wh9OiRbF4iVUiNPymtxkaYOjUab2013zhxo/4ee6ztjyMiIlKt6uvDpbvTp0e31dXB178Ol10W5ksSERFJw4YNcMkl8NJL0W1du8KPfwyf+5wWmxIpEjX+pLQWLIC3386Nde0KY8e2/bEmTozGZs0K80KIiIjUusZG+Na34i/v7dw5LPJx1lnJ5yUiItKkvj7MP/v889FtPXqEuWc/8IHk8xKpYmr8SWk98UQ0Nm5c+yYR33tv6N8/N9bY2Pz8RSIiIrXkV7+CRx+Nxjt1giuvjB85LyIikpTGRvje92DOnOi27beH3/wGRo9OOiuRqqfGn5RWR1fzzWYGRx0VjetyXxERqXVTpsBNN0XjdXXwP/8TP2peREQkSddeC/ffH4137x5G+o0YkXxOIjVAjT8pnYYGeO65aLw9l/k2iRut8OSTsGVL+x9TRESkki1aFJp7+czCyIpJkxJPSUREJMejj8J110XjnTvDz34GBx2UeEoitUKNPymdpUvDHA7ZdtgBBg5s/2MeckgYBp5t48b4kYUiIiLV7s03w4Id+fUW4EtfgpNPTj4nERGRbC+/DN/5Tvy2b387TAUlIiWjxp+UzsKF0djw4R1bnalLFxg/Php//PH2P6aIiEglamyEK66ANWui2044AT796eRzEhERyVZfD5dfHgZr5Dv/fDj11ORzEqkxavxJ6SxYEI0VY96G5i73FRERqSU33wyzZ0fj++0H//VfHTvRJiIiUgxXXQUvvhiNH3UUXHhh4umI1CI1/qR0StX4O+KIMFl5tldegdde6/hji4iIVIKlS+HXv47G+/aFn/40TJQuIiKSpmnT4LbbovEhQ+AHP4i+pxORktBvmpTGxo3w0kvR+AEHdPyxe/UKoxnyzZzZ8ccWEREpd1u2hLmS4ha2+uEPoX//5HMSERHJtn59aO7l69IFrrwSevZMPieRGlWyxp+ZXW9ma8xsQVbsr2Y2J3NbbmZzmrnvcjObn9lP3ZxKtHgxuOfGBg6EPn2K8/ijR0djavyJiEgtuO46eP75aPwTn4AxY5LPR0REJN9PfwpvvBGNX3op7LNP4umI1LJSjvi7ATgxO+DuH3f3Ue4+CrgD+HsL9z8ms29Mh0fKXnMLexRLc42//GajiIhINVm4EP74x2h86FC4+OLE0xEREYmYNg2mTInGx42DM89MPh+RGleyxp+7Pw6si9tmZgacCdxSqueXlJVqfr8mo0ZF54R47TVYvbp4zyEiIlJOGhvD5VGNjbnxurpwOVW3bunkJSIi0mTTJvjRj6LxXr3gu9/VwlMiKUhrjr8jgdfdPWZ5HwAcuN/MZplZi0v9mNmFZjbTzGauXbu26IlKO5W68dejR/wIwlmzivccIiIi5WTy5DCVRr7zzy/OHLoiIiIddf318Oqr0fhXvwq77JJ8PiKSWuPvbFoe7Tfe3Q8BTgIuNrOjmtvR3a9199HuPrpfv37FzlPaY+1aWLMmN1ZXB/vuW9zn0Tx/IiJSKzZsgKuvjsb33hs+97nk8xEREcm3YgXcdFM0PmYMnHZa8vmICJBC48/MOgMfBv7a3D7uvjrzcQ1wJzA2meykKBYtisb23rv4lyAdemg0pnn+RESkGv3ud/D229H4N74BnTsnno6IiEjEz38ODQ25sS5d4IordImvSIrSGPF3HPCcu6+K22hm25tZr6bPgeOBmOtGpWyVemGPJgcdFH2zs2YNrFxZ/OcSERFJy9KlcNtt0fjxx8MhhySfj4iISL6nnoKpU6Pxc86BIUOSz0dE/q1kjT8zuwV4CtjXzFaZ2XmZTWeRd5mvmQ0ws6Zlf3YFpprZXGA68C93v7dUeUoJlHp+vybbbRffUNTlviIiUi3c4ac/jS7o0b07XHppKimJiIjkaGyEq66Kxvv3h3PPTTobEclTsmtD3P3sZuLnxsRWAydnPl8GHFSqvKTEGhvjR/yVovEHYZ6/uXNzYzNnwoc/XJrnExERSdLTT8OMGdH4eedpknQRESkP//xnGJ2e78tfDieqRCRVaS3uIdVqxQp4773cWI8eMHRoaZ6vuQU+NM+fiIhUOnf47W+j8UGD4JOfTD4fERGRfPX1YR7afCNHwqRJyecjIhFq/ElxPf98NLbffmFV31IYOTJMGJtt3Tp4+eXSPJ+IiEhSpk6NXzDry1+Grl2Tz0dERCTf7bfD669H41/5ihb0ECkTavxJccUN8d5vv9I9X7ducOCB0fisWaV7ThERkVJzh2uuicb33ReOOSb5fERERPJt3gw33BCNH3VUWIhRRMqCGn9SXEuWRGN77VXa54y73Dd/3j8REZFK8thj8aPoL7pIIyhERKQ83H57uNoqmxlcfHE6+YhILDX+pLjiRvwNG1ba54w7m6TGn4h0kJmdaGbPm9kSM7s8ZvsOZna3mc01s4Vm9tk08pQq1NgYP1/S8OEwYULy+YhI2VKtktS8/z7ceGM0fsIJsOeeyecjIs1S40+KZ9MmWL06Gi9142/EiOgcgq+8Am++WdrnFZGqZWadgF8DJwEHAGeb2QF5u10MLHL3g4CJwM/MTBOvScc98gi8+GI0rtF+IpJFtUpSdddd0dF+dXVw/vmppCMizVPjT4rnpZeiq+kOGBBW9S2l7bePv5xYo/5EpP3GAkvcfZm71wO3Amfk7eNALzMzoCewDmhINk2pOu7whz9E4yNHwmGHJZ+PiJQz1SpJx5Yt8Kc/ReOTJsHQoYmnIyItU+NPiifuMt+khnmPHBmNzZuXzHOLSDUaCKzM+npVJpbtamB/YDUwH/iKuzfmP5CZXWhmM81s5tq1a0uVr1SLmTPhhReicY32E5Eo1SpJx333wZo10fh55yWfi4i0So0/KZ40G3+a509Eiiuuw5I3pJkTgDnAAGAUcLWZ9Y7cyf1adx/t7qP79etX7Dyl2vzlL9HYyJEwZkzyuYhIuVOtkuS5x8/tN3Fi6ad4EpF2UeNPiieNhT2axDX+Fi+G+vpknl9Eqs0qYHDW14MIoyWyfRb4uwdLgJeA/RLKT6rR8uUwdWo0/qlPabSfiMRRrZLkPfUULFsWjZ97buKpiEhh1PiT4olr/MXNvVcKu+0GO++cG2toCM0/EZG2mwHsbWZ7ZCZBPwuYnLfPCuBYADPbFdgXiPlPWKRAN98cjQ0YEEZRiIhEqVZJ8v7852jskEPCgosiUpbU+JPi2LAhOs9DXV1yk7uaxc/zp8t9RaQd3L0BuAS4D1gM3ObuC83sIjO7KLPbfwNHmNl84CHgm+7+RjoZS8V76y345z+j8bPPjq5cLyKCapWkYMkSmD49Gv/Up5LPRUQK1jntBKRKxA33HjwYunZNLodRo+Dhh3NjavyJSDu5+xRgSl7smqzPVwPHJ52XVKk77ohOT7H99nBG/gKdIiLbqFZJom69NRobMgQmTEg+FxEpmE4hS3GkubBHk+ZW9vX8OY5FRETKSH093HZbNP7hD0OPHsnnIyIikm/9erjnnmhcI9NFyp5+Q6U4liyJxpJu/O27b3SE4VtvwcqVyeYhIiLSFg88AOvW5cbq6uDjH08nHxERkXyTJ8P77+fGevaEU05JJx8RKZgaf1IccZf6Jt3469IFhg+PxufNSzYPESkbZnaJme2Ydh4iLbrzzmjsuOOgf//kcxGRxKlWSdlrbITbb4/GTz9dI9NFKoAaf1Ic5XCpL2iBDxHJ1x+YYWa3mdmJZmZpJySSY9kymDMnGj/rrMRTEZHUqFZJeZs+HVatisY/9rHkcxGRNitZ48/MrjezNWa2ICv2PTN7xczmZG4nN3PfE83seTNbYmaXlypHKZJ168Iltdm6dAmLeyTtoIOiMTX+RGqWu38b2Bv4A3Au8KKZ/a+ZpXBmQiTGXXdFY8OGwYEHJp6KiKRDtUrK3h13RGOHH57O+z0RabNSjvi7ATgxJv7/3H1U5jYlf6OZdQJ+DZwEHACcbWYHlDBP6ai40X5Dh0LnFBaNjhvxt2wZbNiQfC4iUhbc3YHXMrcGYEfgdjP7caqJidTXw7/+FY1/6EOgAT8iNUW1SsrWG2/AY49F4x/5SPK5iEi7lKzx5+6PA+ta3TFqLLDE3Ze5ez1wK3BGUZOT4opr/A0blnweAH36hCXl8y1alHgqIpI+M/uymc0Cfgw8CRzo7l8ADgX0H6uk65FH4J13cmNdu2qidJEao1olZe3uu8Mcf9n69YMjj0wnHxFpszTm+LvEzOZlLgWOm8R2IJC9DOuqTCyWmV1oZjPNbObatWuLnasUohwW9sgWd3nU/PnJ5yEi5WBn4MPufoK7/83dtwC4eyNwarqpSc2LW9Tj2GOhd+/kcxGRNKlWSXlqbIR//CMaP/106NQp+XxEpF2Sbvz9FtgTGAW8CvwsZp+4a1u8uQd092vdfbS7j+7Xr19RkpQ2WrIkGttrr+TzaKLGn4hss4e7v5wdMLObANx9cTopiQArV8LMmdH4hz6UfC4ikjbVKilPzz4bXdTDDM7QBXkilSTRxp+7v+7uWzNnr35PuKw33yoge5bQQcDqJPKTdnCHl16KxtO61Beab/x5s/1jEalew7O/yMwje2hKuYhsE7eox5AhcPDBiaciIqlTrZLyNHlyNDZmDAwYkHwuItJuiTb+zGy3rC8/BCyI2W0GsLeZ7WFmXYGzgJi/OFIW3norunBG167pFoO99oJu3XJj69eH0RUiUhPM7Aoz2wCMNLP1mdsGYA0Qc82KSIK2bg1zJuXToh4iNUW1Ssraxo3w0EPR+Ac/mHgqItIxJWv8mdktwFPAvma2yszOA35sZvPNbB5wDPDVzL4DzGwKgLs3AJcA9wGLgdvcfWGp8pQOevnlaGzwYKhLY/rIjE6dYPjwaHxBXJ9ZRKqRu//I3XsBP3H33plbL3ffyd2vSDs/qXHPPAPr8tY/69wZTtVUXiK1RLVKytpDD8HmzbmxXr1g4sRU0hGR9utcqgd297Njwn9oZt/VwMlZX08BppQoNSmmuMbf7rsnn0e+ESNg9uzc2Pz5cPLJ8fuLSFUxs/3c/Tngb2Z2SP52d58dczeRZNx7bzR25JGwY9yaZyJSrVSrpKz985/R2AknhKu7RKSilKzxJzUirvE3dGjiaUSMGBGNacSfSC35D+AC4heRcuADyaYjkrFpEzzySDR+0knJ5yIiaVOtkvL02mswa1Y0rpHpIhVJjT/pmHId8Re3wMcLL4Th6t27J5+PiCTK3S/IfDwm7VxEcjz2WGj+ZevVCyZMSCcfEUmNapWUrXvuicaGDImfTklEyp4af9Ix5dr469cPdt0VXn99W2zrVnjuORg1KrW0RCQZZvbhlra7+9+TykUkR9ybqWOP1aVTIjVItUrKknt8rTrlFC1AJVKh1PiT9mtogFWrovEhQ5LPJc6BB+Y2/iDM86fGn0gtOK2FbQ7ozZQk76234KmnonFd5itSq1SrpPy8+CIsWxaNq1aJVCw1/qT9Vq8Oo+iy7bgj9O6dTj75DjwQHnwwNzZ/fjq5iEii3P2zaecgEvHAA9DYmBvbZRc4+OB08hGRVKlWSVmKW4Bq5EgYMCD5XESkKNT4k/ZbvjwaK4fLfJvEzfOnBT5EaoKZfcrd/2xmX4vb7u4/Tzonkdg3UyeeCHV1yeciIqlTrZKy09gI990XjZ94YvK5iEjRqPEn7Veu8/s12Xdf6NQpd1TimjXhtssu6eUlIknYPvOxV6pZiDRZtQrmzYvGdemUSC1TrZLyMn9+dKqkujqYNCmdfESkKNT4k/Yr98Zft26h+bdoUW58/vwwkbqIVC13/13m4/fTzkUEiB9BsddesPfeyeciImVBtUrKzv33R2PjxoXpnESkYunaEmm/uMbf0KGJp9GiESOiMc3zJ1IzzGyYmd1tZmvNbI2Z/cPMhqWdl9Sg/DlnQaP9RARQrZIy0dgYX6uOPz75XESkqNT4k/Yr9xF/oHn+RORm4DZgN2AA8DfgllQzktqzYkVYJTGf3kyJSKBaJembMwfefDM31qULTJyYRjYiUkRq/En7bNgA69blxjp1goED08mnOXGNv0WLoKEh+VxEJA3m7je5e0Pm9mfA005KaszDD0djBxwAu+2WfC4iUo5UqyR9DzwQjR1+OPTSFJQilU6NP2mfFSuisYEDoXOZTRs5cCD06ZMbq6+PH3khIlXDzPqaWV/gETO73MyGmtnuZnYZ8K+085Ma89BD0ZjmmhWpeapVUjYaG+Nr1XHHJZ+LiBRdmXVppGJUwvx+AGZh1N8TT+TG58+H/fdPJycRScIswmgJy3z9+axtDvx34hlJbVq9GhYvjsY/8IHkcxGRcqNaJeVhzpzo1VxdusBRR6WSjogUlxp/0j7Ll0djQ4YknkZBRoyINv4WLIAzz0wnHxEpOXffI+0cRID4y3z32QcGD04+FxEpK6pVUjbiatVhh0HPnsnnIiJFp8aftE8lLOzRRAt8iNQ0MxsBHAB0b4q5+43pZSQ1RZf5ikgBVKskNY2N8Y0/1SqRqqHGn7RPJTX+DjggXPLrWXMkr1gB77wDO+yQXl4iUnJm9l1gIuHN1BTgJGAqoDdTUnpr1oSpJfLpMl8RyaJaJalavDjUq2ydOukyX5EqUrLFPczsejNbY2YLsmI/MbPnzGyemd1pZn2aue9yM5tvZnPMbGapcpR2amyMX9yjHOf4gzBEfY+YKyk06k+kFnwUOBZ4zd0/CxwEdEs3JakZcSMohg2Lr0kiUstUqyQ9cbVqzBjo3Tv5XESkJEq5qu8NwIl5sQeAEe4+EngBuKKF+x/j7qPcfXSJ8pP2eu21sDJutp49Yccd08mnEHGX+8aNwhCRarPJ3RuBBjPrDawBhqWck9QKXeYrIoVRrZJ0uMMjj0TjGpkuUlVK1vhz98eBdXmx+929IfPl08CgUj2/lFDcaL/ddw+X05YrNf5EatXMzOjy3xNWT5wNTE81I6kNb74ZVknMpzdTIhKlWiXpeOml6Hs7Mzj66HTyEZGSSHOOv88Bf21mmwP3m5kDv3P3a5NLS1pVSfP7NYlr/C1cGC5brivlwFcRSZO7fzHz6TVmdi/Q293npZmT1IgnnsidWxZgyBDYa6908hGRsqVaJal59NFobORI2GmnxFMRkdJJpeNhZv8JNAB/aWaX8e5+CGFi24vNrNmZRc3sQjObaWYz165dW4JsJaISG3977AE9euTG3n03/lhEpKqY2YfN7OfAl4A923C/E83seTNbYmaXN7PPxMx8tAvN7LFi5SxV4PHHo7GJE8t7dLyIpEa1SlIR1/ibODHpLESkxBJv/JnZOcCpwCfd80+FB+6+OvNxDXAnMLa5x3P3a919tLuP7tevXylSlnwrV0ZjQ4Ykn0db1NXB8OHRuC73FalqZvYb4CJgPrAA+LyZ/bqA+3UCfk04AXUAcLaZHZC3Tx/gN8Dp7j4c+Fhxs5eKtXkzPPNMNK5Lp0QkhmqVpGLNGli0KBpX40+k6iR6qa+ZnQh8Ezja3Tc2s8/2QJ27b8h8fjzwgwTTlNbEjZIr98YfhMt9Z8zIjS1YAKefnk4+IpKEowmLSjmAmf2J8MaqNWOBJe6+LHO/W4EzgOz/kD8B/N3dV8C/T1aJwPTp8P77ubE+feKnnRARUa2SNMSNTB82DAYPTj4XESmpko34M7NbgKeAfc1slZmdB1wN9AIeyAw3vyaz7wAzm5K5667AVDObS5jU9l/ufm+p8pQ22rIlrOqbrxIKxIgR0ZhG/IlUu+eB7DMTg4FC5k0aCGQPb16ViWXbB9jRzB41s1lm9pm4B9KUFDUo7s3UkUdqTlkRaY5qlSSvuSkpRKTqlGzEn7ufHRP+QzP7rgZOzny+DDioVHlJB73ySlgQI9vOO0fnzytHcY2/pUth48bKyF9ECmZmdxMWitoBWGxmTasjjgWmFfIQMbH86Sk6A4cCxwLbAU+Z2dPu/kLOncICVdcCjB49OnaKC6kijY3xb6aOana6YhGpUapVkpqNG6NXQoFqlUiVSnNVX6lE+cu9Q2Vc5gvQty8MHBial00aG8PqvmPGpJeXiJTCTzt4/1WEERdNBgGrY/Z5w93fA94zs8cJJ65eQGrXokWwbl1urGtXGDcunXxEpJypVkk6nn46XMmVbeed4YAD4vcXkYqma06kbSq58Qfx8yvpcl+RquPujzXdgOcI00z0AhZnYq2ZAextZnuYWVfgLGBy3j7/AI40s85m1gMYBywu3lFIRYob7TdmjEaWi0iEapWkRlNSiNQU/WZL21R642/kyGhs7tzk8xCRRJjZmYT5Yj8GnAk8Y2Yfbe1+7t4AXALcR3iDdJu7LzSzi8zsosw+i4F7CfMwTQeuc/cFpTkSqRiPxbxX12q+ItIC1SpJVGMjTJ0ajR95ZPK5iEgiCrrU18zuAK4H7nH3xtb2lyq2cmU0VgkLezQ5KGb6yPnzQwHUGS6RavSfwJimVQzNrB/wIHB7a3d09ynAlLzYNXlf/wT4SdGylcr2yith7th8EyYkn4uIVBLVKknOggXw9tu5sa5dYezYVNIRkdIrtNPxW8JS8C+a2ZVmtl8Jc5JyVukj/vbaC7bbLje2fn38cYlINahreiOV8SYa7S6lEnfp1P77wy67JJ+LiFQS1SpJTtxov3HjoHv35HMRkUQUVFDc/UF3/yRwCLAceMDMppnZZ82sSykTlDKyeTO8/npuzAwGDUonn/bo1AmGD4/G581LPhcRScK9ZnafmZ1rZucC/yJvZIRI0TzxRDSmFRJFpHWqVZKcuFqly3xFqlrBZ5LMbCfgXOB84FngF4RG4AMlyUzKz6pV0diuu0K3bsnn0hGa50+kJpiZAb8EfgeMJKxieK27fzPVxKQ6bdwIs2dH42r8iUgLVKskUa+/Di++GI1rSgqRqlboHH9/B/YDbgJOc/dXM5v+amYzS5WclJlKv8y3SVzjTyP+RKqOu7uZ3eXuhwJ/TzsfqXLTp0NDQ25sl11gn33SyUdEKoJqlSQq7jLfffbRlBQiVa7QEX/XufsB7v6jpqafmXUDcPfRJctOyku1NP4OPDAae+mlMNefiFSbp81sTNpJSA2IezM1fnyYEkNEpGWqVZIMreYrUpMKbfz9T0zsqWImIhWgWhp/O+wAQ4dG4wsWJJ6KiJTcMYQ3VEvNbJ6ZzTczDfGV4nKHJ5+MxsePTz4XEalEqlVSevX1YXR6Pl3mK1L1WrzU18z6AwOB7czsYKDptHVvoEeJc5Nys3JlNDZ4cPJ5FMPIkbB8eW5s7lw44ohU0hGRkjkp7QSkBrz4Iqxdmxvr3BnGjk0nHxGpNKpVUnozZ8L77+fG+vSJX/hQRKpKa3P8nUBY0GMQ8POs+AbgWyXKScpVtYz4g9D4mzw5N6Z5/kSqhpntQqhTewHzgR+5u67nl9KIG+13yCHQQ+dIRaR5qlWSqLhadcQRUFfwep8iUqFa/C139z+5+zHAue5+TNbtdHfX5LO15L334M03c2N1dTBgQDr5dFTcAh8LFsDWrcnnIiKlcCPwHvAroCdhxUSR0tBlviLSPqpVkgxNSSFS01q71PdT7v5nYKiZfS1/u7v/POZuUo3iLvMdMAC6dEk+l2IYOhR69YING7bFNm2CpUu1AqNIdejv7v+Z+fw+M5udajZSvdavjx8xrjdTItI61SpJxsqVsGpVbqyuDg47LJ18RCRRrY3r3T7zsSfQK+YmtaKaLvOFUOjiVvedOzf5XESkFMzMdjSzvmbWF+iU97VIcTz9NDQ25sYGDIDdd08nHxGpJKpVkoy40X4jRoRFD0Wk6rU44s/df5f5+P1k0pGyVW2NPwiX+06blhubOxc+9rF08hGRYtoBmMW2RakAmkZSODAs8YykOsW9mZowAcyicRGRXKpVkozmapWI1ITWFvcAwMx+DPwPsAm4FzgIuDRzGbDUgmpt/OXTiD+RquDuQ9POQWpAY2P0BBLoMl8RKYhqlSRi82aYHXMV+RFHJJ+LiKSi0CV8js+sMHUqsArYB/hGS3cws+vNbI2ZLciK9TWzB8zsxczHHZu574lm9ryZLTGzywvMUUopbo6/wYOTz6OYRoyIrmL16qvw2mvp5CMiIpXluefgrbdyY127wqGHppOPiIhIvlmzoL4+N9a3r+Y1F6khhTb+mlZwOBm4xd3XFXCfG4AT82KXAw+5+97AQ5mvc5hZJ+DXwEnAAcDZZnZAgXlKqcSN+Kv0+Yt69ID99ovGn302+VxERKTyxF06NXo0dO+efC4iIiJx4mrV4YdHB0CISNUq9Lf9bjN7DhgNPGRm/YDNLd3B3R8H8huEZwB/ynz+J+CDMXcdCyxx92XuXg/cmrmfpGX9enjnndxYly7Qv386+RTTwQdHY2r8iYhIIZ56KhrTZb4iIlJOVKtEal5BjT93vxw4HBjt7luA92hfM25Xd38185ivArvE7DMQyL6udFUmFsvMLjSzmWY2c+3ate1ISVr18svR2MCB1XGWKK7xN2dO4mmISOmY2QQz+2zm835mtkfaOUkVWL8eFiyIxjVnkoi0g2qVlMTKldEpm+rqYNy4dPIRkVQUtLhHxv7AUDPLvs+NRc4Hcle1auLN7ezu1wLXAowePbrZ/aQDqvEy3yajRkVjy5bB229Dnz4JJyMixWZm3yWMVt8X+CNh6oo/AzrVLR0zfXpY3CPboEGVP/+tiCROtUpKJm603/DhsMMOyeciIqkpaMiWmd0E/BSYAIzJ3Ea34/leN7PdMo+5G7AmZp9VQPZ/zYOA1e14LimWuBF/1dL469MHhg2LxjXqT6RafAg4nTBSHXdfDfRKNSOpDnGr+R5+ePJ5iEg1UK2S0lCtEhEKH/E3GjjA3Ts6om4ycA5wZebjP2L2mQHsnRne/gpwFvCJDj6vdEQ1N/4gXO67bFlubPZsmDgxlXREpKjq3d3NzAHMbPu0E5Iq4B4/ikJvpkSkfVSrpPjq62HmzGhc8/uJ1JxCJ2lbALRpJQczuwV4CtjXzFaZ2XmEht8kM3sRmJT5GjMbYGZTANy9AbgEuA9YDNzm7gvb8txSZHGNvyFDks+jVDTPn0g1u83Mfgf0MbMLgAeB36eck1S6pUshf17hzp3Dir4iIm2nWiXFN2cObM5bj7N3b9h//1TSEZH0FDrib2dgkZlNB95vCrr76c3dwd3PbmbTsTH7rgZOzvp6CjClwNyklBobq3uOP4hv/D33HGzcCD16JJ+PiBSNu//UzCYB6wlzJ33H3R9IOS2pdHGXTh18sGqGiLSLapWURHOX+VbDAo0i0iaFNv6+V8okpIytWROGiWfr2RN23DGdfEph111hwABYnTWVZGMjzJsHhx2WXl4i0mFm9lXgb3oDJUX19NPRmC7zFZF2Uq2SktCUFCKSUVC7390fA5YDXTKfzwBmlzAvKRfNXeZrcYsvV7C4UX/PPpt8HiJSbL2B+8zsCTO72Mx2TTshqXAbN8bXhyOOSD4XEakWqlVSXGvWhGkp8mlQg0hNKnRV3wuA24HfZUIDgbtKlJOUk7jG39ChiadRcmr8iVQld/++uw8HLgYGAI+Z2YMppyWVbNYs2LIlN9avH+y5Zzr5iEjFU62Soosbmb7PPrDzzsnnIiKpK/QC/4uB8YR5J3D3F4FdSpWUlJG4+f2qaWGPJoccEo0tWBC9zFlEKtUa4DXgTVS/pCOau3Sq2kbCi0gaVKukOHSZr4hkKbTx9767/7sDYmadAS9NSlJW4kb8VdPCHk0GD4a+fXNj9fWwaFE6+YhIUZjZF8zsUeAhwkJVF7j7yHSzkorW3GTpIiLtpFolRdXYCM88E42rVonUrEIX93jMzL4FbJdZceqLwN2lS0vKRq00/szC5b4PPZQbnzULRo1KJSURKYrdgUvdfU7aiUgVWLkSVq3KjdXVwbhx6eQjItVCtUqKZ+FCWL8+N7bddnDQQenkIyKpK3TE3+XAWmA+8HlgCvDtUiUlZaK+Hl59NRofPDj5XJJw6KHR2PTpyechIh1mZr0zn/4YWGFmfbNvaeYmFSzu0qnhw6F372hcRKQVqlVSEnG1aswY6NIl+VxEpCwUNOLP3RvN7C7gLndfW9qUpGysWgWed0X3LruEM0bVaMyYaGzePNi8Gbp3Tz4fEemIm4FTgVmEqSmyJ2BzYFgaSUmFi5ssXZdOiUj7qVZJ8cU1/rSar0hNa7HxZ2YGfBe4hFCIzMy2Ar9y9x8kkJ+kqVYu820ydGhY6eqNN7bFtmyBuXN1GZdIhXH3UzMf90g7F6kSW7bAjBnRuBp/ItJOqlVSdOvXh0t98x1xRPK5iEjZaO1S30sJq/mOcfed3L0vMA4Yb2ZfLXVykrJaa/yZwdix0bgu9xWpWGb2UCExkVbNnQubNuXGevcOl/qKiHSAapUUzfTpYXGPbIMGhZuI1KzWGn+fAc5295eaAu6+DPhUZptUsxUrorEhQ5LPI0lxl/vGjfAQkbJmZt0z8yPtbGY7Zs2ZNBQYUOBjnGhmz5vZEjO7vIX9xpjZVjP7aJHSl3IUd+nU2LFhcQ8RkXZQrZKi08rzIhKjtTn+urj7G/lBd19rZpodtNotXx6NVfOIP4hv/C1eHIbNa/J2kUryecKo9QGEuZOa5k1aD/y6tTubWafMfpOAVcAMM5vs7oti9vs/4L6iZS7lKa7xp0unRKRjVKukeNw1F62IxGrtNHV9O7dJNYgb8Vftjb/+/aOrFrvDrFnp5CMi7eLuv8jMmfR1dx/m7ntkbge5+9UFPMRYYIm7L3P3euBW4IyY/b4E3AGsKV72UnbefBNeeCEa12TpItIBqlVSVC+9BGvyXuJOnWD06HTyEZGy0dqIv4PMbH1M3AAtc1rN1q+Ht9/OjXXuDLvtlko6iRozBlauzI3NmAHHHJNOPiLSbu7+KzMbARxAVt1y9xtbuetAIPsPwSrCHLf/ZmYDgQ8BHwBihgtL1YgbQTFsWFjpXkSkg1SrpCjiRqYfdBD06JF8LiJSVlps/Ll7p6QSkTITt7DHoEHhrFG1GzsW/v733JgW+BCpSGb2XWAi4c3UFOAkYCrQ2pspi4l53tdXAd90961mcbv/O4cLgQsBhlT7PKnVSpf5ikgJqVZJUahWiUgzNCO1xKvFy3ybxA2HX748OnReRCrBR4Fjgdfc/bPAQUC3Au63Csi+7n8QsDpvn9HArWa2PPM8vzGzD+Y/kLtf6+6j3X10v3792n4Ekq7GRs2ZJCKlplolHbN5M8yeHY2rVokIavxJc+JG/NVK469PH9hnn2h85szEUxGRDtvk7o1Ag5n1JsxvNKyA+80A9jazPcysK3AWMDl7h8w8TEPdfShwO/BFd7+rqNlL+p57Ljr1RbducPDBqaQjIlVJtUo6ZvZsqM+bgr9vX9h773TyEZGyknjjz8z2NbM5Wbf1ZnZp3j4TzeydrH2+k3SeNa8WV/TNNnZsNKbLfUUq0Uwz6wP8nrBi4myg1V9md28ALiGsgLgYuM3dF5rZRWZ2UQnzlXITN9rv0EOha9fkcxGRaqVaJR0Td5nvYYdBncb5iEjri3sUnbs/D4yCfy8t/wpwZ8yuT7j7qQmmJtleeikaq7XG35//nBubPj2s8NvC/CgiUl7c/YuZT68xs3uB3u4+r8D7TiHMtZQdu6aZfc/tSJ5SxqZNi8Z06ZSIFJFqlXRYXK3S/H4ikpF44y/PscBSd4+5rlRSs2VL/Bx/wwq54qBKjBoVFjLZunVbbM0aWLYM9twztbREpDBmdkhL29w9ZiIckTwbNsC8mPfeejMlIkWgWiVFsXp1dJomMxg3Ln5/Eak5aTf+zgJuaWbb4WY2lzBB7dfdfWHcTlqBqgRWrsxteAHstBP07p1OPmno0SM0/2bNyo1PnarGn0hl+FkL2xz4QFKJSAV75pmwuEe2AQNA/2+ISHGoVknHxV3mu//+sOOOyeciImUptcZfZgLa04ErYjbPBnZ393fN7GTgLiB2ZlJ3vxa4FmD06NH5y9dLeyxbFo3V0mi/JhMmRBt/Tz4J55yTTj4iUjB3PybtHKQKNHfplKZ8EJEiUK2SotCUFCLSijRH/J0EzHb31/M3uPv6rM+nmNlvzGxnd38j0QxrlRp/wfjx8Itf5MbmzIH162tr9KNIBTOzz8TF3f3GpHORCuOuOZNEJBGqVdJuW7bAjBnR+PjxyeciImUrzcbf2TRzma+Z9Qded3c3s7GE1YffTDK5mqbGX7DHHuGSrtWrt8UaG8OlX5MmpZeXiLTFmKzPuxPmlp0N6M2UtOzFF+GNvPONXbrA6NHp5CMi1Uy1Stpn3jzYuDE31qsXDB+eTj4iUpZSafyZWQ9gEvD5rNhF8O9VqD4KfMHMGoBNwFnurst4kxLX+Ntjj+TzSJtZOFv2t7/lxqdOVeNPpEK4+5eyvzazHYCbUkpHKkncaL+DDw5zwIqIFJFqlbTbk09GY4cdFhYpFBHJSKXx5+4bgZ3yYtdkfX41cHXSeQnQ0BC/om+tLmgxYUK08TdtWhj5V1eXTk4i0hEbaWbOWJEcusxXRNKjWiWF0fx+IlKAtFf1lXKzcmVo/mXr2xd22CGdfNJ26KHQtSvU12+LvfUWLF6sIfQiFcDM7iasjAhh2ogDgNvSy0gqwnvvwdy50bgafyJSAqpV0i5r1sCSJdG4Gn8ikkeNP8n10kvRWC1e5tuke3cYMyY6jP7JJ9X4E6kMP836vAF42d1XpZWMVIhnnoGtW3Nj/fvXdj0UkVJSrZK2ixvtt88+0K9f8rmISFnTtYqSK25+v1q9zLdJ3KpYU6cmn4eItJm7P+bujwHPAouBjWbWN+W0pNw99VQ0dsQRYe5XEZEiU62SdtGUFCJSIDX+JJcW9oiaMCEaW7QI1q1LPhcRaRMzu9DMXgfmATOBWZmPIvHc4ydL15spESkR1Spps4YGePrpaFy1SkRi6FJfyRXX+Bs2LPk8ysmAAaH5mX8Z9JNPwmmnpZOTiBTqG8Bwd38j7USkQixdGuZNytapE4wdm04+IlILVKukbebOhY0bc2M9e8LIkenkIyJlTSP+ZJutW+Hll6PxWm/8Qfyov0cfTTwNEWmzpYTVEUUKEzeVw6hR0KNH4qmISM1QrZK2iatVhx0GnTWuR0Si9JdBtlm1CrZsyY316QM77phKOmXlyCPhpptyY089FVZ+3H77dHISkUJcAUwzs2eA95uC7v7l9FKSsvb449HYkUcmn4eI1BLVKmmbuMafLvMVkWao8Sfb6DLf5o0aBX375s7rV18fiu4JJ6SWloi06nfAw8B8oDHlXKTcvf02zJ8fjavxJyKlpVolhVu9OjoFEcQvSCgighp/kk2Nv+bV1cExx8Add+TGH3pIjT+R8tbg7l9LOwmpENOmhcU9sg0ZArvvnk4+IlIrVKukcHGj/Q44AHbaKflcRKQiaI4/2UaNv5Yde2w0NnVqdGJdESknj2RWS9zNzPo23dJOSsrUE09EY3FzvIqIFJdqlRQurvGnWiUiLdCIP9kmbsj4Hnskn0e5OvTQMOfh229vi9XXh9V9J01KKysRadknMh+vyIo5oLMakquhIYz4y6fLfEWk9FSrpDAbN8KMGdG4Gn8i0gI1/iRobITly6PxPfdMPJWy1alTuNz3zjtz4w89pMafSJlyd529kMLMmRMWbMq2/fZhjlcRkRJSrZKCTZ8eXYxxp51gv/3SyUdEKoIafxKsWhVGr2Xr3Vsr+uY79tho42/qVNi8Gbp3TycnEWmWmX0mLu7uNyadi5S5uMt8Dz8cunRJPhcRqSmqVVKwuJXnx48P85GLiDRDjT8JliyJxoYNA7Pkcylno0eHhuj69dtimzeHy8M+8IH08hKR5ozJ+rw7cCwwG9CbKckV1/jTZb4ikgzVKmldY2P8/H5HHZV8LiJSUdT4k+C556KxffZJPo9y17kzTJwIkyfnxh98UI0/kTLk7l/K/trMdgBuSikdKVcrVoRbNjM44oh08hGRmqJaJQVZtAjWrcuNdekCY8emk4+IVAyNCZYgrvGnuSLiHXdcNDZ1Krz/fvK5iEhbbQT2TjsJKTNxIygOPFDTXYhIWlSrJCruMt8xY6BHj+RzEZGKohF/Au6weHE0rsZfvDFjoFcv2LBhW2zjRnj0UTjhhNTSEpEoM7ubsDIihJNdBwC3pZeRlKXHHovGtEKiiCREtUoK8uij0djRRyeehohUnlQaf2a2HNgAbAUa3H103nYDfgGcTDjjda67z046z5qxdi289VZurEuXMMefRHXpElb3zb/cd/JkNf5Eys9Psz5vAF5291VpJSNl6K234Nlno3HN7yciyVGtkpatWgXLlkXjqlUiUoA0R/wd4+5vNLPtJMLw9r2BccBvMx+lFOIu89177zCfncQ79dRo42/6dHjtNejfP52cROTfzGwvYFd3fywvfqSZdXP3pSmlJuXm8cfDhOnZBg6EvfZKJx8RqRmqVVKwuJHpBxwAu+ySfC4iUnHKdY6/M4AbPXga6GNmu6WdVNXS/H5td/DB4Y1hNnf417/SyUdE8l1FGFmeb1Nmm0jw8MPR2Ac+oFXtRSQJV6FaJYXQZb4i0gFpNf4cuN/MZpnZhTHbBwIrs75elYlFmNmFZjbTzGauXbu2BKnWADX+2s4MTjstGr/77tAAFJG0DXX3eflBd58JDE0+HSlL774bRmvnO+aY5HMRkVqkWiWtW7cO5syJxidOTDoTEalQaTX+xrv7IYRLei82s6PytsedZo/tprj7te4+2t1H9+vXr9h51gY1/trn1FOjI0JWrYqfK0pEkta9hW3bJZaFlLcnn4QtW3JjO+8MI0akk4+I1BrVKmnd449HBxYMGqT52EWkYKk0/tx9debjGuBOYGzeLquAwVlfDwJWJ5NdjVm3DtasyY116qS5jQrRv39Y4Tff3Xcnn4uI5JthZhfkB83sPGBWCvlIOXrooWjsmGOgrlxnQhGRKqNaJa3TlBQi0kGJr95gZtsDde6+IfP58cAP8nabDFxiZrcSFvV4x91fTTjV2hA32m/PPaFr1+RzqUSnnx69TOzBB+Eb34AePdLJSUQALgXuNLNPsu3N02igK/ChtJKSMrJ5M0ybFo3rMl8RSc6lqFZJSzZsiJ+SQpf5ikgbpLFs666EAtf0/De7+71mdhGAu18DTAFOBpYAG4HPppBnbdBlvh1zzDHQs2eYJ6rJpk1hFEncHIAikgh3fx04wsyOAZqu2/yXu8ecNpea9PTTofmXrXdvOPTQdPIRkZqjWiWteuIJaGjIjfXrpykpRKRNEm/8ufsy4KCY+DVZnztwcZJ51Sw1/jqmWzc4/nj4+99z43fcocafSBlw90eAR9LOQ8pQ3KVTEyeG6S5ERBKkWiXN0pQUIlIE+otR69T467jTT4/GFiyAeZFF2kSkgpjZiWb2vJktMbPLY7Z/0szmZW7TzCxyUkvK1JYtYRRFPl3mKyIVRrWqir33Hjz1VDR+3HHJ5yIiFU2Nv1q2fj2szlszpa4O9t47nXwq1fDhsO++0fjNNyefi4gUhZl1An5NWH3+AOBsMzsgb7eXgKPdfSTw38C1yWYp7TZjRpg3KVuPHjBuXDr5iIi0g2pVlXvsMaivz4317QujRqWSjohULjX+alncaL+hQ2G77RJPpaKZwSc/GY0//DC8qjVpRCrUWGCJuy9z93rgVuCM7B3cfZq7v5X58mnCCvRSCe69NxqbMEELW4lIpVGtqmYPPhiNHXusLvMVkTbTX41apst8i2fSJNhpp9xYYyPcdls6+YhIRw0EVmZ9vSoTa855wD1xG8zsQjObaWYz165dW8QUpV02bYJHYqbS0qVTIlJ5VKuq1fr18SvPT5qUfC4iUvHU+KtlavwVT5cucOaZ0fidd8LGjcnnIyIdZTExj90xrMZ4HvDNuO3ufq27j3b30f369StiitIujz0Wmn/ZevUKI/5ERCqLalW1euSR+NV8dZmviLSDGn+1bMGCaEyNv/b7yEeil4m9+y7cfXc6+YhIR6wCBmd9PQhYnb+TmY0ErgPOcPc3E8pNOmLKlGjsuON0ma+IVCLVqmp1T8zAzEmTdJmviLSL/nLUqtdei1/YI26RCilMnz5wyinR+C23hMt+RaSSzAD2NrM9zKwrcBYwOXsHMxsC/B34tLu/kEKO0lbr1sHTT0fjJ52UfC4iIh2nWlWN1qyBWbOi8RNPTD4XEakKavzVqtmzo7H99oPtt08+l2py9tnR2KpV8ZPzikjZcvcG4BLgPmAxcJu7LzSzi8zsosxu3wF2An5jZnPMbGZK6Uqh7r8/eiKmf39dOiUiFUm1qkrdey943hXbgwfD/vunk4+IVLzOaScgKZkZU/MPPTT5PKrNsGFw2GHRESXXXBNW4erUKZ28RKTN3H0KMCUvdk3W5+cD5yedl3RA3GW+J52kS6dEpGKpVlUZd/jXv6Lxk04Ci5vSUUSkdfpPt1bFDR9X4684zjknGluxIr6Ii4hIMlasgEWLonFd5isiIuXi+edh6dJoXLVKRDpAjb9a9Npr8MorubG6Ol3qVCxjxsDo0dH4738P9fXJ5yMiIvETpe+zTxipLSIiUg7++c9obOTIcKmviEg7qfFXi5qb369nz+RzqVZf/GI09uqrcNddiaciIlLzGhvjR12ffHLyuYiIiMSpr4+fkuLUU5PPRUSqihp/tUjz+5XeyJFw5JHR+B/+AJs3J5+PiEgte+qp6Er2ZnDCCenkIyIiku/RR2H9+txY164waVIq6YhI9VDjrxZpfr9kfOEL0dibb8JttyWfi4hILfvb36Kxww+Hfv2Sz0VERCRO3JVBxx4LvXolnoqIVBc1/mpNc/P7HXxwOvlUs332iT9Dd911sHZt8vmIiNSi1avhySej8Y99LPlcRERE4qxcCdOnR+NnnJF8LiJSddT4qzXNze+3/fbJ51ILPv/50FjNtnEj/Oxn6eQjIlJrbr8d3HNjAwbA+PHp5CMiIpLv9tujsSFDdFWWiBRF4o0/MxtsZo+Y2WIzW2hmX4nZZ6KZvWNmczK37ySdZ9WKm98vbgVaKY6hQ+GDH4zGH3wQpk1LOhsRkdry/vvxl0595CPRkzIiIiJp2LwZ7r47Gv/wh8N8tCIiHZTGf70NwH+4+/7AYcDFZnZAzH5PuPuozO0HyaZYxTS/X/IuuQR23DEav/JKLfQhIlJKDzwQP1G6Lp0SEZFycc898bXqtNPSyUdEqk7ijT93f9XdZ2c+3wAsBgYmnUdNam5+v1GjUkmnZvTuDV/9ajS+enVY5VdEREojblGP446DPn0ST0VERCTCHW69NRo/4QTYYYfk8xGRqpTqdS5mNhQ4GHgmZvPhZjbXzO4xs+HJZlal4iaM1fx+yTjpJBgzJhq/8UZ44YXk8xERqXaLFsHChdH4mWcmn4uIiEicp5+GpUuj8Y9/PPlcRKRqpdb4M7OewB3Ape6eN7aZ2cDu7n4Q8CvgrhYe50Izm2lmM9dqpdSWPfhgNKbLfJNhBpdfDl265Ma3bg3xjRvTyUtEpFrdcEM0tt9+MFznEkVEpEzcdFM0NmpUqFciIkWSSuPPzLoQmn5/cfe/52939/Xu/m7m8ylAFzPbOe6x3P1adx/t7qP79etX0rwr2ttvhzNK+Y4+OvFUatbuu8O550bjK1bAj34UXXVSRETa54UX4OGHo/GPfUwTpYuISHlYtCj+iqxPfSr5XESkqqWxqq8BfwAWu/vPm9mnf2Y/zGwsIc83k8uyCj30EDQ25sZ23RVGjkwnn1r12c/CXntF4/fcA5MnJ5+PiEg1uvbaaGyXXcK0CyIiIuXgj3+MxoYMgaOOSj4XEalqaYz4Gw98GviAmc3J3E42s4vM7KLMPh8FFpjZXOCXwFnuGg7VIffdF40df3xY3EOS07VrWM13u+2i2/7v/2DJkuRzEhGpJs8/D48+Go2fe274GywiIpK2F1+ERx6Jxj/zGb0/E5Gi65z0E7r7VKDF62zc/Wrg6mQyqgFr1sCzz0bjJ5yQfC4CQ4fCFVfAd76TG6+vh69/Ha6/Hvr2TSU1EZGK19xovw9+MPFUREREYl1zTTS2yy5wyinJ5yIiVU+nE2rBAw9E548bMgT23TedfAROPhlOPz0aX7UKvvQleO+95HMSEal0zz0Hjz0WjX/ucxrtJyIi5WH+/Phade650YUARUSKQI2/WhB3me8JJ2iC87RddhkMGxaNP/98GPlXX598TiIilex3v4vGdt01/kSLiIhI0tzhqqui8V131ch0ESkZNf6q3YoVYcWofLrMN33du8NPfgK9e0e3zZgB//Vf0QVZREQk3tSp8MQT0fh552m0n4iIlIeHHoK5c6PxCy5QrRKRklHjr9rdf380ts8+YZ45Sd/uu4ezft26Rbc99BB885vw/vuJpyUiUlE2boQf/Sga798fTjst+XxERETybdoEP/95ND5smGqViJSUGn/VrLER7rknGj/xxORzkeaNHAk//nH8Cl6PPAIXXwzr1yefl4hIpfj1r+H116PxL35R8yWJiEh5uPbasOhivi9/GTp1Sj4fEakZavxVswcfhJdfjsYnTUo+F2nZ+PHw3e/Gb5szB84/P/5NrYhIrZs/H267LRofNw5OOin5fERERPItWAB/+Us0PmFCuImIlJAaf9WqoQF++9to/JBDYLfdks9HWnfKKWHBjzjLlsEnPwlPPplsTiIi5WzLFvjv/46uXN+tG3zrW1rESkRE0rdpE3zve9G5u7t2DQv6iYiUmBp/1eruu2Hlymj8gguSz0UKd+aZ8L//C507R7e9/TZ85SthbhCt+CsiAr/6VTgxku8LX4CBA5PPR0REJN9PfgLLl0fjF14IgwYlno6I1B41/qpRfT38/vfR+NixMGZM8vlI2xx/PPzyl9CjR/z2m2+Gc8+FhQsTTUtEpKzcfnv4e5hv//3h7LOTz0dERCTfP/4BkydH4/vvD5/+dPL5iEhNUuOvGt1+e/zEsRdfnHwu0j5jx8J118HOO8dvf+EFOOcc+MEPYN26ZHMTEUnbU0+FRZHy1dXBt7+tSdJFRCR9M2eGK3nydesG3/++apWIJEaNv2qzcSNcf300PnEiDB+eeDrSAfvsE0azHHFE8/tMngwf/GBoEmrlXxGpBUuXwuWXR+dKArjkEth33+RzEhERybZoUZi/b+vW6LbLLoNhw5LPSURqlhp/1aSxMYwAe/vt3LgZfPGLqaQkHdS3L1x1FXz1q/Hz/kFo9l5zTVgc5P/9v/jRniIi1WDhwjB6/b33ots++EFdNiUiIumbPz/MNfvuu9Ftp5wCp5+efE4iUtPU+Ksmv/gFPPhgNH7SSTqrVMnq6sKKvn/8I+y5Z/P7bdoEf/kLnHpqWATkgQe0CIiIVI/77gsLVL3xRnTbmDFhFKBW8RURkTTdf38YcBF3gurgg+E//1O1SkQS18wQIqk4t94amj75unaFz38++Xyk+PbfP1z6e8cdYYRfc5f2NjbCk0+GW69ecOSRMGECHH54+FpEpJI0NMC118ZPYwEwdCj83/81PypaRESk1Orrw1U6t90Wv33IkLC6b9euiaYlIgJq/FU+d7j7bvjZz+K3/9d/wcCByeYkpdOpE5x5Zlj597e/hTvvjJ/nqsmGDTBlSrjV1cHIkTBqFBx0ULj17p1Y6iIibeIOjzwCV18NK1bE79OvX3ijpb9lIiKShoaG8H/2ddfB6tXx++yxR/i/vU+fRFMTEWmixl8le+mlMMph5sz47RdfHC7zlerTpw9ccQWce24Y6XnnnfD++y3fp7ER5swJtyYDB4ZFRPbeO1xGPHgwDBoEPXqULncRkZa8/34YsfznP8O8ec3vt//+4aTXLrskl5uIiNS2xsYwn/q6dWEBjz/8AV55pfn999wzNP369k0sRRGRfGr8VZrNm2HWLHjssbCia0ND/H4f/nBoCkl12223sGLY+eeHSwv+8Q94/fXC7//KK+H2yCO58Z12Co+9yy6w665hVE3fvuHWp0+49eoF228fRhKKiLRXYyOsXAnPPQdPPAGPPx4WLWrJccfB974H3bsnkqKIiFSx+vrQyIu7vfkmvPXWto9vv93y1TbZJk2Cb387/L8sIpKiVBp/ZnYi8AugE3Cdu1+Zt90y208GNgLnuvvsVh/4/fdh6dLiJ1wM7tHPsz82Nobb1q2wZUtYqGHz5rAa1Ouvh9srr4RVolpbsGHCBPjmNzVxbC3p0wcuvDA0AGfNgn/+Ex56KPwMtcebb4Zba+rqoGfPMEIw+9a9+7Zbly7QrVv42LVr+Ni5c/ytri7csj9vuplFP8bdID7WJHuf7I/5n+dr7fepFL9v+h1OVUlqVTnXqdbE1bHsr5tuTfWsoSHUtIaGUNM2bgx/k955JyzQ8cYbobYtXRq2F8IsLPBxwQX6/RARoYTvqyqZe1hcI65xl/2xqbkXtxBHR3TuDF/7GnzsY6pVIlIWEm/8mVkn4NfAJGAVMMPMJrv7oqzdTgL2ztzGAb/NfGzZsmXw8Y8XPeeKMmkSfOc7YS44qT11dWF1yzFj4FvfCpeBT50abq++Wvzna2wMi4w0t9CISIUqWa1SnWq/0aPDiuX77592JiIiZaGk76sq2Ve+AtOmpfPc48eH6Zb22Sed5xcRiZHGiL+xwBJ3XwZgZrcCZwDZBeoM4EZ3d+BpM+tjZru5ewk6F1ViwAC47LIw2k8Ewii78ePD7bLLwqV0c+bA3Lnhtnx52hmKlDPVqnKx557hTdzhh2vkhIhILtWqODvskPxzHnFEuPpmxIjkn1tEpBVpNP4GAiuzvl5F9KxT3D4DgUiBMrMLgQsBDqrF5dG7doVzzgnz+XXrlnY2Uq7MYMiQcDv99BDbuDFcYvfii+G2YkVoDr72WuFzl4hUr6LVqpqvU+3Rsyccc0wYxX7YYZpLVEQkXklq1ZAhQ4qeaKJKvZBGz57b5r4eOjT8bz1yZGmfU0SkA9Jo/MWdrvd27BOC7tcC1wKM3n772H2qTt++YeTD+PHhDVHv3mlnJJWoRw848MBwy7ZlS2j+rVmzbX7JpvlQ3norzIWyfj1s2FD4vFwiladotaom61Rb9ewZLovab78wVcG4ceHEloiItKQ0tWr06MquVW1t/NXVhfmym5p5O+0EO+7Y/EfVJxGpMGk0/lYBg7O+HgSsbsc+Ud26wbBhHc2vdOIWEWj6WFcX5uWrqwvFJHtxhJ13hv79w23QoHBmSaMfpFS6dIHBg8OtNVu2hAmRN27c9nHz5txbfX3uraEh3G/Llm0T/2d/bFrkpmmBgKZb06IB7mE75Maavs6+NYlbUCf7Y5yWFjJoad9iKcVjJmXWrLQzKIbS1Kpyr1OtaWkxnOxFd5oW6Wm6de8O220XbttvH+raTjuFj4MGhVXEdRmviEhble59VSXr2ze8n2qpkde0rW/fcGmw3luJSBVLo/E3A9jbzPYAXgHOAj6Rt89k4JLMPBXjgHcKmodi2DC47bYipysizerSJZwh7dMn7UyknFRHA6c0tUp1SkREiqd076sq2SmnwKmnVsv/IyIiHZZ448/dG8zsEuA+wrLz17v7QjO7KLP9GmAKYcn5JYRl5z+bdJ4iIlK7VKtERKTcqVY1Q6P3RERypDHiD3efQihC2bFrsj534OKk8xIREWmiWiUiIuVOtUpERFqj0yEiIiIiIiIiIiJVSI0/ERERERERERGRKqTGn4iIiIiIiIiISBVS409ERERERERERKQKqfEnIiIiIiIiIiJShSws9FQdzGwD8HzaeSRkZ+CNtJNIiI61etXS8dbSse7r7r3STqIc1Vidgtr6udexVq9aOt5aOlbVqmaoVlU1HWv1qqXjraVjLUqt6lyMTMrI8+4+Ou0kkmBmM3Ws1aeWjhVq63hr7VjTzqGM1Uydgtr7udexVqdaOt5aO9a0cyhjqlVVSsdavWrpeGvtWIvxOLrUV0REREREREREpAqp8SciIiIiIiIiIlKFqq3xd23aCSRIx1qdaulYobaOV8cqUHvfm1o6Xh1r9aql49WxCtTe96aWjlfHWr1q6Xh1rG1UVYt7iIiIiIiIiIiISFBtI/5EREREREREREQENf5ERERERERERESqUkU0/szsRDN73syWmNnlMdvNzH6Z2T7PzA4p9L7lpoPHutzM5pvZnGIt+1xqBRzvfmb2lJm9b2Zfb8t9y00Hj7WiXtsCjvWTmZ/feWY2zcwOKvS+5aaDx1pRrysUdLxnZI51jpnNNLMJhd630qlW5WxXrSrwvuVGtSpnu2oVlfe6gmpVS1SrcrZXTa2qpToFqlV521WrqLzXFRKuVe5e1jegE7AUGAZ0BeYCB+TtczJwD2DAYcAzhd63nG4dOdbMtuXAzmkfR5GPdxdgDPBD4OttuW853TpyrJX22hZ4rEcAO2Y+P6nKf2djj7XSXtc2HG9Pts0fOxJ4rhJf2xJ9b1SrvGp/7lWrKuy17cjf7yp9XVWrKvC1LdH3RrXKK+vnviN/uyvtde3o8Vbpa6taVWGvaxuOt2i1qhJG/I0Flrj7MnevB24Fzsjb5wzgRg+eBvqY2W4F3recdORYK1Grx+vua9x9BrClrfctMx051kpTyLFOc/e3Ml8+DQwq9L5lpiPHWokKOd53PVORgO0BL/S+FU61KpdqVYH3LTOqVVlUqyqWalXzVKtyVUutqqU6BapVqlWBalUbXttKaPwNBFZmfb0qEytkn0LuW046cqwQfhDuN7NZZnZhybIsno68PtX42rakkl7bth7reYSzre25b9o6cqxQWa8rFHi8ZvYhM3sO+Bfwubbct4KpVhW+T1X+3JfgvmlQrWqealVlvK6gWtUS1arC96mkn/taqlOgWqVaFahWtXLfbJ07lGoyLCbmBe5TyH3LSUeOFWC8u682s12AB8zsOXd/vKgZFldHXp9qfG1bUkmvbcHHambHEP5oN81XULWva8yxQmW9rlDg8br7ncCdZnYU8N/AcYXet4KpVhW+T1X+3JfgvmlQrYrbUbWqkl5XUK1qiWpV4ftU0s99LdUpUK1SrVKtavNrWwkj/lYBg7O+HgSsLnCfQu5bTjpyrLh708c1wJ2EIaDlrCOvTzW+ts2qsNe2oGM1s5HAdcAZ7v5mW+5bRjpyrJX2ukIbX59Msd3TzHZu630rkGpVgftU+899Ee+bBtWqPKpVFfe6gmpVS1SrCtynwn7ua6lOgWqVapVqVdtfWy+DiQ1buhFGJS4D9mDbxIXD8/Y5hdyJWacXet9yunXwWLcHemV9Pg04Me1j6ujxZu37PXInoq2617aFY62o17bAn+MhwBLgiPZ+n8rh1sFjrajXtQ3HuxfbJqE9BHgl8/eqol7bEn1vVKuq9Oc+a9/8v99V99q2cKwV9dp28O931b2uLRxrRb2ubThe1SrVqpaOtaJ+7jv4t7uiXtciHG/VvbYt/P2uqNe2g8daUa9rG463aLUq9QMu8JtyMvACYeWS/8zELgIuynxuwK8z2+cDo1u6bznf2nushBVd5mZuCyvhWAs83v6EjvZ64O3M572r9LWNPdZKfG0LONbrgLeAOZnbzJbuW8639h5rJb6uBR7vNzPHMwd4CphQqa9tCb43qlXV+3OvWlWBr217/35X6euqWlWhr20JvjeqVRX4c9/ev92V+Lp25Hir9LVVrarA17XA4y1arWrqHoqIiIiIiIiIiEgVqYQ5/kRERERERERERKSN1PgTERERERERERGpQmr8iYiIiIiIiIiIVCE1/kRERERERERERKqQGn8iIiIiIiIiIiJVSI0/kSIys0fN7IS82KVm9psW9h+dTHYiIiKqVSIiUv5Uq0SKR40/keK6BTgrL3ZWJi4iIlIOVKtERKTcqVaJFIkafyLFdTtwqpl1AzCzocAA4BNmNtPMFprZ9+PuaGbvZn3+UTO7IfN5PzO7w8xmZG7jM/GjzWxO5vasmfUq8bGJiEh1UK0SEZFyp1olUiSd005ApJq4+5tmNh04EfgH4azUX4Efufs6M+sEPGRmI919XoEP+wvg/7n7VDMbAtwH7A98HbjY3Z80s57A5qIfkIiIVB3VKhERKXeqVSLFoxF/IsWXPSy9aTj6mWY2G3gWGA4c0IbHOw642szmAJOB3pmzUE8CPzezLwN93L2hSPmLiEj1U60SEZFyp1olUgRq/IkU313AsWZ2CLAd8BbhLNKx7j4S+BfQPeZ+nvV59vY64HB3H5W5DXT3De5+JXB+5jmeNrP9SnAsIiJSne5CtUpERMrbXahWiXSYGn8iRebu7wKPAtcTzkr1Bt4D3jGzXYGTmrnr62a2v5nVAR/Kit8PXNL0hZmNynzc093nu/v/ATMBFSgRESmIapWIiJQ71SqR4lDjT6Q0bgEOAm5197mEoegLCUXryWbucznwT+Bh4NWs+JeB0WY2z8wWARdl4pea2QIzmwtsAu4p/mGIiEgVU60SEZFyp1ol0kHm7q3vJSIiIiIiIiIiIhVFI/5ERERERERERESqkBp/IiIiIiIiIiIiVUiNPxERERERERERkSqkxp+IiIiIiIiIiEgVUuNPRERERERERESkCqnxJyIiIiIiIiIiUoXU+BMREREREREREalC/x9NQ8n85ADfAwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.stats import lognorm as my_dist                                   # import traingular dist as my_dist\n",
    "dist_type = 'Log Normal'                                                     # give the name of the distribution for labels\n",
    "mu = np.log(0.10); sigma = 0.2                                               # given the distribution parameters\n",
    "\n",
    "x_values = np.linspace(0.0,0.3,100)                                          # get an array of x values\n",
    "p_values = my_dist.pdf(x_values, s = sigma, scale = np.exp(mu))              # calculate density for each x value\n",
    "P_values = my_dist.cdf(x_values, s = sigma, scale = np.exp(mu))              # calculate cumulative probablity for each x value\n",
    "\n",
    "plt.subplot(1,3,1)                                                           # plot the resulting PDF\n",
    "plt.plot(x_values, p_values,'r-', lw=5, alpha=0.8); plt.title('Sampling the ' + str(dist_type) + ' PDF, $f_x(x)$'); plt.xlabel('Values'); plt.ylabel('Density')\n",
    "plt.xlim([0.0,0.3])\n",
    "\n",
    "plt.subplot(1,3,2)                                                           # plot the resulting CDF\n",
    "plt.plot(x_values, P_values,'r-', lw=5, alpha=0.8); plt.title('Sampling the ' + str(dist_type) + ' CDF, $F_x(x)$'); plt.xlabel('Values'); plt.ylabel('Cumulative Probability')\n",
    "plt.xlim([0.0,0.3])\n",
    "\n",
    "p_values = np.linspace(0.00001,0.99999,100)                                        # get an array of p-values\n",
    "x_values = my_dist.ppf(p_values,  s = sigma, scale = np.exp(mu))             # apply inverse to get x values from p-values\n",
    "plt.subplot(1,3,3)\n",
    "plt.plot(x_values, p_values,'r-', lw=5, alpha=0.8, label='uniform pdf')\n",
    "plt.xlim([0.0,0.3])\n",
    "\n",
    "plt.subplots_adjust(left=0.0, bottom=0.0, right=2.8, top=0.8, wspace=0.2, hspace=0.3); plt.title('Sampling the Inverse the ' + str(dist_type) + ' CDF, $F^{-1}_x(x)$'); plt.xlabel('Values'); plt.ylabel('Cumulative Probability')\n",
    "\n",
    "print('The mean is ' + str(round(my_dist.mean(s = sigma, scale = np.exp(mu)),4)) + '.') # calculate stats and symmetric interval\n",
    "print('The variance is ' + str(round(my_dist.var(s = sigma, scale = np.exp(mu)),4)) + '.')\n",
    "print('The interval at alpha level ' + str(round(1-level,3)) + ' is ' + str(np.round(my_dist.interval(alpha = level,s = sigma, scale = np.exp(mu)),2)))"
   ]
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    "There are many other parametric distributions that we could have included.  Also we could have demonstrated the distribution fitting. \n",
    "\n",
    "#### Comments\n",
    "\n",
    "This was a basic demonstration of working with parametric distributions. \n",
    "\n",
    "I have other demonstrations on the basics of working with DataFrames, ndarrays, univariate statistics, plotting data, declustering, data transformations, trend modeling and many other workflows available at [Python Demos](https://github.com/GeostatsGuy/PythonNumericalDemos) and a Python package for data analytics and geostatistics at [GeostatsPy](https://github.com/GeostatsGuy/GeostatsPy). \n",
    "  \n",
    "I hope this was helpful,\n",
    "\n",
    "*Michael*\n",
    "\n",
    "#### The Author:\n",
    "\n",
    "### Michael Pyrcz, Associate Professor, University of Texas at Austin \n",
    "*Novel Data Analytics, Geostatistics and Machine Learning Subsurface Solutions*\n",
    "\n",
    "With over 17 years of experience in subsurface consulting, research and development, Michael has returned to academia driven by his passion for teaching and enthusiasm for enhancing engineers' and geoscientists' impact in subsurface resource development. \n",
    "\n",
    "For more about Michael check out these links:\n",
    "\n",
    "#### [Twitter](https://twitter.com/geostatsguy) | [GitHub](https://github.com/GeostatsGuy) | [Website](http://michaelpyrcz.com) | [GoogleScholar](https://scholar.google.com/citations?user=QVZ20eQAAAAJ&hl=en&oi=ao) | [Book](https://www.amazon.com/Geostatistical-Reservoir-Modeling-Michael-Pyrcz/dp/0199731446) | [YouTube](https://www.youtube.com/channel/UCLqEr-xV-ceHdXXXrTId5ig)  | [LinkedIn](https://www.linkedin.com/in/michael-pyrcz-61a648a1)\n",
    "\n",
    "#### Want to Work Together?\n",
    "\n",
    "I hope this content is helpful to those that want to learn more about subsurface modeling, data analytics and machine learning. Students and working professionals are welcome to participate.\n",
    "\n",
    "* Want to invite me to visit your company for training, mentoring, project review, workflow design and / or consulting? I'd be happy to drop by and work with you! \n",
    "\n",
    "* Interested in partnering, supporting my graduate student research or my Subsurface Data Analytics and Machine Learning consortium (co-PIs including Profs. Foster, Torres-Verdin and van Oort)? My research combines data analytics, stochastic modeling and machine learning theory with practice to develop novel methods and workflows to add value. We are solving challenging subsurface problems!\n",
    "\n",
    "* I can be reached at mpyrcz@austin.utexas.edu.\n",
    "\n",
    "I'm always happy to discuss,\n",
    "\n",
    "*Michael*\n",
    "\n",
    "Michael Pyrcz, Ph.D., P.Eng. Associate Professor The Hildebrand Department of Petroleum and Geosystems Engineering, Bureau of Economic Geology, The Jackson School of Geosciences, The University of Texas at Austin\n",
    "\n",
    "#### More Resources Available at: [Twitter](https://twitter.com/geostatsguy) | [GitHub](https://github.com/GeostatsGuy) | [Website](http://michaelpyrcz.com) | [GoogleScholar](https://scholar.google.com/citations?user=QVZ20eQAAAAJ&hl=en&oi=ao) | [Book](https://www.amazon.com/Geostatistical-Reservoir-Modeling-Michael-Pyrcz/dp/0199731446) | [YouTube](https://www.youtube.com/channel/UCLqEr-xV-ceHdXXXrTId5ig)  | [LinkedIn](https://www.linkedin.com/in/michael-pyrcz-61a648a1)\n"
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